1. Managing your Tower Bux
You get Tower Bux for building a new floor, finding a Bitizen when prompted, and sometimes for moving a Bitizen in the elevator to the right floor. Especially early on, it can take a while to stock up on Tower Bux.
The first thing you should save up for is buying all the elevators. By doing so you'll transport Bitizens and VIPs around in less time, and by the time you can afford the third and final elevator, you'll have a tower high enough to want to speed things up as much as possible.
The third elevator is not really that much faster than the second one, but as you reach tower level 25-30 you'll regret not having it. The downside is that because it's still pretty fast, it can be annoying to move the elevator down one floor -- it tends to overshoot. If you need to do that, just move it down two floors and tap it once or twice to move it up slightly and land on the right floor.
Once you have all the elevators, how you spend your Tower Bux is down to how you play the game. I tend to spend them on speeding up construction of new floors, but if you have 6-8 hours to wait and are about to go to bed, you're better off saving those Bux by waiting until you wake up again.
Other than speeding up construction, keep 5-10 Bux in stock at any time to move floors around (See section 2.) and to speed up stocking goods or sell them instantly when needed (See section 5.). Alternatively, you can use them to instantly sell a type of good (See section 3.) that takes 2+ hours to stock before you go to bed. When you wake up, it will be ready to generate you more money.
After you get the third elevator and get around 60 Tower Bux, trade them in for $100,000. You'll have money and spare Bux to use for whatever requires it at any time. There is no reason to ever trade in anything less thatn 50 Bux, since over time it will be less efficient. Even if you trade in 20 Bux and instantly buy and complete a new floor, you won't recoup the $50k you miss out on by doing so in the long run. Unless you play the game really casually and never play it more than 3 minutes at a time.
2. Managing your Tower layout
As you start out, you'll likely end up constructing new floors and not having many issues with how they are organized. It will become a mix of different floors all stacked on top of each other, which leads to a lot of scrolling up and down in a few days. When your tower becomes rather high, it's time to organize everything properly.
Moving all residential floors to the bottom makes it easier to manage your Bitizens' jobs. If they are not at their job, you'll also know where to find them easily.
Moving the different types of shopping floors together will also save you some time. Try to put shops of the same type on top each other, with the fastest-stocking shops at the bottom. This will make it easier to know where to look when only a few goods sell out, as you won't get any indication that one good is out of stock and the goods that stock fast also stock less of it -- and sell out faster.
Once you've done this, it's time to dress up your Bitizens. It might be fun to give them all funny hats, beards, and glasses, but that comes at a cost of efficiency. How will you quickly find them if they all look the same or completely different, unless you memorize every single one of them? A good idea is to dress them up according to the color of their shop they work at. It only costs $1 to change their appearance randomly, so money is no issue by the time you'll want to organize everything.
The way I did this was to give every employee of the same type of shop glasses, beards, hats, or different color shirts. Keep in mind that women can't have beards or moustaches (boo!), but you can always dress up the female Bitizens with the color of that shop type. So I have a couple of floors with Bitizens that all have hats, Bitizens that all glasses, and Bitizens with color-coded shirts so I know where they'll be.
Once you've done this, it will never take more than 10 seconds to find any Bitizen for quick Tower Bux. If they are not in the couple of floors of the right color or dress attachment, they will be in the couple of residential floors at the bottom of the tower. At worst you'll only have to tap on a bunch of floors in a row if they are halfway outside the screen, instead of going up and down your entire tower if you can't find them.
3. Managing your Bitizens
The colored numbers indicate your Bitizen's skill level in that type of shop. This only means that they will give you that percentage off stocking a good. Having three level 9 Bitizens in one store gives you 27% off, etc.
Dream jobs are more valuable than that, regardless of the skill level. Giving a Bitizen their dream job not only gives you an instant 3 Tower Bux (you keep it if you evict or move them afterwards), but it also stocks twice the amount of goods for the same cost. Every additional dream job Bitizen gives you the x2 multiplier for an extra good, up to three.
If you are impatient or need to go to sleep, don't be afraid to spend a Tower Bux here and there to stock a shop and be able to move jobs around. Moving a normal level 9 Bitizen out of a store to replace it with a dream job Bitizen will always pay off in the end. The more goods you stock, the more they will sell and the less often you have to micromanage re-stocking those goods. Moving them before bed time means you'll wake up with more stocked goods and don't have to re-stock them as much afterwards.
When you have Bitizens with no skill levels above 7 and no dream-job you can place them in, you can always evict them. You'll never know what kind of floor you'll end up with unless it's a residential floor, so it's not worth saving them up in most cases. However, if you already have two or three Bitizens with the same dream job for a store you don't have yet, it can be worth to keep them employed elsewhere and wait.
When you have three Bitizens in their dream job and get a new one with the same dream job, just evict whoever has the lowest skill level and replace them. Yes, you'll be a dick for doing so but it's ok to be the evil landlord in this game.
If you have just built a new floor and the only unemployed Bitizen you have left only has skill level 0 for that job, don't keep him in storage just because he's not a good fit. He can still stock goods and make you money -- you can live without the maximum 9% off the price. But always look if there's another Bitizen who has a high skill level for two shops and no place for his dream job, and move that it to the newly constructed floor. Then put the first unemployed Bitizen in the open spot that was created. This may take some time to manage, but you'll end up with the best workforce in the end.
Finally, Bitizens will only move into a residential floor is there is an open spot. Early on, it can pay off to evict anyone who is not level 9, preferably spread across multiple residential floors so the chance of a new Bitizen moving in is increased. Later on, you'll need to play it for long stretches at a time to get them to move in all. Just use Tower Bux to fill up a new floor as needed, and keep one or two open spaces in case someone does want to move in. You'll probably earn 10 Bux in the time you'd wait for that random move-in. Evict whoever is useless.
4. What floor should I build next?
You will always need to have enough residential floors so you can have 3 Bitizens at work everywhere. The best good in a shop gives you $3 per sold unit and net you the most profit, so always fill up the shop workforce.
There's five types of shops that each have three slots for Bitizens, and residential floors can house five Bitizens. You'll want an equal amount of floors for each shop type to equalize demand for goods. This demand will always go back to 100 if you keep building new shop types and residential floors, so don't worry about demand too much.
Ideally, you will have 3 times as many residential floors as you have shop floors of one type. Since there are a 5 shop types that can each contain 3/5th the amount of Bitizens of a residential floor, you will only need 3 times as many residential floors as you have of any shop floor -- provided you built them in equal distribution.
If math is hard for you, just go to the Stats screen and look at the floor distribution. Then multiply the amount of floors for any shop by 3 to reach the amount of residential floors you need. If you have a distribution of 2/2/2/2/2 or 4/4/4/4/4 for shops, that means you'd need 6 or 12 residential floors. Easy no?
Always build a new residential floor first if you have an equal distribution of shop floors, or you won't have anyone to work in the next shop floor! New Bitizens might move in while you save for the next shop, and those in turn might yield you more profits or goods storage if you're lucky.
5. Damn those VIPs, I always waste them!
This is a common problem. The first thing you should learn is to not select them in the Lobby unless you know you can use them. Construction VIPs wear a yellow helmet, and VIPs that take 3 hours off stocking goods wear a brown postal outfit. Chances are you'll have a floor under construction 90% of the time, or a good that takes 1h+ to stock.
If you want to maximize these VIPs, save them if you can build a floor in the next ten minutes, or potentially use a Tower Bux to sell out a good that's nearly sold out and takes less than 3 hours to stock. Provided you keep an eye on your tower that would cost you 1 Tower Bux, in exchange for a new fully stocked good and not having to keep an eye on that good for a long time.
The hard part is when you have to distinguish between extra-customer VIPs (they wear glasses) and VIPs that instantly buy up one type of good.
Between the latter two, always take a look at your shop floors that take the longest to stock. They will have the highest amount of goods to sell (depending on how much has been sold already) and make the best targets in general. Just check a couple of shops, see if there is one that has a lot of all three kinds of goods stocks, and dump the VIP in there.
For advanced tactics, look at which shop is fully stocked while everything else is being stocks. Dumping the VIP there might sell out one of the goods, allowing you to re-stock it again.
6. Look, I really don't have time to play this all day
That's ok, not many people do. Notifications can help you if you're at work or studying, but they can distract just as much. You also don't want to hear "TING" when you are just falling asleep. Keep in mind you'll only get one notification after you close the game, so if you tap Close it can be to forget about the game afterwards.
There are a couple of shops, especially the food shops, that have a very low stocking time. You could technically destroy them so you only have other shops to manage if you are short on time during the day, but one of the reasons to keep playing Tiny Tower is to get as high a tower as possible.
In the end, it comes down to your own play-style and how much time you have. If you can play all day, just stock some 40+ minute goods before making dinner. And just because a good takes 5 minutes to stock doesn't mean you should obsess over it. They will sell out quick and the income is not worth the hassle.
If you're a management buff, go all out and tailor everything for efficiency. If you just want to make a tower that looks fun, you can do that too. Try to find a middle road between "fun looking" and efficiency if you can, since looks don't get you paid in this game.
Last but not least, someone over on the Touch Arcade forums has created a spreadsheet with all data you could possibly need!