With everything set up for running (hoses attached, vent open), you should be able to hear fuel entering the carb when you squeeze the primer bulb. If in doubt, pull the hose at the carb, and look for flow (same as you can do to check fuel pump operation when engine is running).
If you can properly prime the carb with the bulb, but know you are getting no flow with the engine running (nothing coming out of the line to carb), replace or rebuild the pump. If you have one of the larger pumps supplied on electric start models, the rebuild kit is 0438618 — easy rebuild. If you have one of the little square pumps, you can get a kit and rebuild it (0393088), or just replace the pump (I recommend the latter with the little pump because of its size and complexity, but that’s a matter of preference).