Never let anyone else write with your Parker pen, not even to try it out for a few seconds. Really. High-quality nibs adapt to your (unique) hand position and writing style, and even a little trial scribbling from someone else can compromise this. It is especially important not to do this if the other person writes with the opposite hand than yours.

Don't overfill the Parker pen with ink. When filling it, get into the habit of drawing a full amount of ink into the pen, then releasing three or four drops into the inkwell and drawing back air. This will pull the huge pool of ink that is clinging to the nib from being dipped into the inkwell back into the pen. Flooded nibs can bleed or just drop pools of ink onto the paper. A flooded nib can also get jostled when the pen is closed and spray ink all over the inside of the cap, which will end up on your hands when you next use the Parker fountain pen.

Store Parker pen vertically (nib up, eg: in a shirt pocket), whenever you can. Leaving it horizontal for long periods of time can cause excess ink to flow into the nib.

Leave your Parker writing instrument at home when you fly - the changes in cabin pressure can cause pens to leak and discharge ink all over your luggage, shirt pocket, or whatever. If you must take your pen with you, empty it completely first. Travel with a small ink bottle with a really tight cap, and put the entire ensemble in a sealed plastic baggie wrapped in a paper towel, in case it leaks.

Leave the cap on whenever you can. The nib will dry out and clog if the cap is off for long periods.

If your Parker fountain pen does dry out (symptoms: ink doesn't start right away, pen seems to write badly or skips), empty it out and soak it in cold water, preferably with a few drops of ammonia. (I use a squirt or two of ammonia-based window cleaner like Windex). Draw the water in and out several times, and (ideally) let it soak for a while. Then empty it out and fill with ink as usual.

Use Parker pen for regular writing. The more you use it (correctly), the better and smoother it will write. If you leave it unused for weeks, it can take a while to get the ink started again.

A good fountain pen (which Parker definitely is) should glide effortlessly over the paper, which is the whole joy of using it. If it shows resistance, skips or has trouble getting started, you're either out of ink, or it has dried out and clogged, or both.

Don't lose it. Most fountain pens of acceptable quality are expensive, and since they're small they are quite easy to lose or misplace. Get into the habit of having a regular place for the Parker pen.