Assuming the pump is gummed up: This happens to me after the engine sits for a few months. I usually blow on the vent line and flip the prop, that usually loosens up the sticking parts. I just did this on my friend's plane and it worked. If it's a slightly gummed up carb, this usually works to break it free. After that it's good for the entire season.

The other thing I've seen is to make sure your choke is sealing off air. If it's leaking the engine will not draw the fuel it needs to start.