If a fountain pen is not used for an extended period, the nib and feed will dry out. If you leave it long enough, the ink in the cartridge/converter/whatever can actually evaporate. How long this takes depends on the pen and the ink.
If the pen has been idle for a while and is reluctant to start writing, here are some techniques that can be used to get it restarted.
1. If the pen uses a converter (or is a piston filler), you can force ink into the section and nib by twisting the filling knob until a drop of ink form on the feed, and then reversing the twist to draw that drop back into the pen. Obviously, you want to hold the pen over a bit of paper towel (and never over clothing or white carpets) when you do that. In theory, you could squeeze the cartridge in a cartridge filler to achieve the same effect, but that's a less precise maneuver.
2. Hold the pen over a sink with the nib and feed in a stream of running cool water for a few seconds. This will tend to dissolve dried ink in the nib and feed.
3. With a converter or piston filler, you can simply refill the pen (with the same ink). Twist the knob to expel the unused ink back into the bottle, and then refill the reservoir completely. I find that it helps to do this a couple of times so that you flush out any dried ink.
4. Periodically, its a good idea to flush out a pen completely using fresh water. Slightly warm water is best, but you don't want the water so hot that it is likely to soften any plastic or rubber components of the pen. Using a converter, force fresh water through the nib and feed until it runs clear. Dry off the exterior, and then refill the pen. If you are using a cartridge, it's probably a good idea to let the pen sit empty for a few hours to dry out completely - any water left inside the section or fee will dilute the ink and your initial usage of the pen will be fainter than normal. If you are using a cartridge or piston filler, just fill the reservoir, then expel that ink back into the bottle, and refill again. The minute amount of water in the pen won't affect an entire bottle of ink to any noticeable degree (and some inks actually like to be diluted a bit with water).
5. In extreme cases, you may need to let the nib, feed and section soak in a water bath for a few hours, or even use an ultrasonic cleaner (with clear water) to clean out the inside of the components. It is also sometimes necessary to 'floss' out the ink channel in the feed using either a fine knife or a brass shim. This is specialized work and is best left to an experienced pen technician.