Feel free to add your own suggestions.
Getting On:
Think Soup Nazi, don't waste other people's time (both that of those in line and in the bus driver's seat) by scrounging for your cash/bus pass. Have it ready, or stand far enough away that you can scrounge without bothering others.
If you're really cheap, you can use a tactic my mother employed once in the good old days, take a transfer (those paper dealys they hand out with a timestamp) and flash it at drivers even after it has expired. Usually they'll either not notice or not care and let you on, if they do notice and care, the worst that happens is you have to pay regular fare.
Choosing a Seat:
With public transporation it's all about avoiding the freaks. To do this, take seats next to people you won't mind sitting next to. Befriending someone on your route is a great way to stay safe, or, you can be sneaky. Befriend your backpack/suitcase, prop it up next to you; conversation with it is not necessary, but certainly helps keep others away. Prop your feet up and sleep (or pretend to sleep while listening to music) on a two-seater bench for near-gauranteed immunity from having to sit next to anyone. You can also be aggressive. Sit right next to someone who looks timid and has available space to scrunch. Intimidate them into their scrunch zone and then sprawl on your freshly conquered territory. (Note: this will make you unpopular).
As people board, you may lose your buffer of people you don't mind sitting next to. Learn who these people are and avoid them in preference of those who leave after you get off. You can also try fighting fire with fire, dress and/or act like a freak yourself. This will scare others away and give you free reign, sadly, it may also attract freaks to your presence. Use caution.
The Bus Driver:
Bus drivers range from the veteran nice dudes to Bus Nazis. The nice kind will pick you up if you chase after the bus, let you off in more convenient places, and even announce stops over the intercom if they spot you dozing off. The Bus Nazis will not do any of these things, they will also tend to demand exact change only even if you're near-broke and you need to get home desperately.
If you converse with your driver by sitting in the front row, you can scope out what kind you have. If he's a Nazi, all is lost. Only time will either get them fired or mold them into a nice driver. You can try social engineering on them nonetheless but it's usually a fruitless effort. If you have a nice driver, talking them will get them to be extra nice to you. Sometimes after talking to a nice driver for awhile they'll regularly stop at where you prefer to get off and other such neat stuff. I had one nice driver give me free rides after he learned that I had been paying an extra 25 cents by accident for the past few months.
Sleep:
The true mark of a veteran bus rider is if they have the courage to sleep on the bus. If you have a Bus Nazi the only possible way to pull this off and not miss your stop is if you learn to time your route, if you have a nice bus driver he'll usually wake you up with the intercom when you arrive at your stop. Again, find out what kind you have before attempting this. How long you stay on your route is also of obvious importance, in my cae, my route is about 20 minutes long, and I don't sleep, per se, but I do relax, rest and am generally not fully concious for the duration of the trip.
Getting Off:
I find the most effective method of departure is to stand up, put one foot foreward (but not on the ground) and wait for the bus' weight to catch up with it. When it does, you'll fly to the front -- or into the back of somebody if you're not looking, be careful. Thank the bus driver and step out. Congratulations! You now know How to ride a bus.