The most important thing to remember is that umbrellas expand your personal space. You need to be aware that you’re taking up more room, and act accordingly. Don’t try and barge past groups of people while carrying an umbrella; someone will get injured. Ditto if you suddenly decide to open a large umbrella on a busy street corner. And above all, remember that people who are taller than you can get hit in the face or stabbed in the cornea by your umbrella. You staying dry is not more important than whether the tall dude standing next to you keeps his eyesight.
The second thing to remember is that you might not be wet, but your umbrella probably is. Don’t dump it on the seat next to you on the bus or train; that’s effectively rendering the seat useless for other people. Even if you’re holding on to it, bear in mind that it can easily drip water onto other people. It’s not difficult to take a plastic bag with you so you can wrap up your umbrella when it’s not in use. Failing that, put it on the floor. It’s already wet and dirty, so who cares that it’s down there?
If you’re on public transport. don’t hang it over the back of the seat in front; it’ll dig into the person sitting in that seat. If you regularly take buses or trains, a golf-sized umbrella is generally a bad idea.
The third thing to remember is that not everyone else has an umbrella, and the people that don’t want to get out of the rain quickly. The fact that you have an umbrella is not an excuse to linger dazed, especially when waiting to cross the street.
Finally, if you’re grabbing your umbrella from a stand at a shop or restaurant, remember that umbrellas look alike, so check to make sure you have the right one. And don’t be a skank and grab the one you wish was yours instead.