I have been writing nearly exclusively with fountain pens for a number of years - over a decade now (almost two decades...). I found a cheap one in high school and was hooked. I have yet to loose a shirt to one - though there have been a few fingers covered in ink. I just made my first one, so I am learning new things, but here are some things I have picked up along the way...
Always carry with the pen capped and the tip up. If you have a habit of tapping your pen, tap on the base, not the tip! When flying, I put my pens in a ziplock bag and stick them in snugly in my briefcase. I have yet to have an issue on a plane, but better safe then sorry. Storage is best capped and up, but capped and flat is usually fine too. Just not uncapped, and not tip down!
Don't loan your fountain pens out, even for a quick signature! Your pen tends to "learn" your style, and loaning it out can lead to a pen that does not perform as you expect when you get it back. Also, people who don't use fountain pens tend not to know how to write with one - especially when it is formed to your preferences. I always have a rollerball loaner in my briefcase. I tend to care more about this issue then is warranted, but that's how I was taught and I'm sticking to it!
If your pen starts loading up with ink, dripping when you write or leaking into the cap, it needs to be cleaned. Ditch the cartridge, take off the nib and run it under water until the water runs clear. Give it a good shake and rinse again. When the water is clear and you can't shake more droplets out GENTLY dry with paper towels and load in a fresh cartridge. If its dripping after cleaning lot you may have other issues.