It's best as mentioned, if you have the time, clean the grease channel. Good winter time, rainy day job type of thng... If in a pinch for time, remove zerk, and clean hole as best you can. Be sure and pump a bit through the zerk before installing to make sure it is clear.
Spray some type of lubricant in the hole. WD-40, PB Blaster, whatever you have on hand... Install the zerk, and start pumping. You'll probably feel some resistance, but keep pressure on it. The thin liquid, 99% of the time will find a way out, and grease right behind it. Just keep your hand on the handle, clear of anything it may hit. When it breaks loose, it breaks loose, right now...
On a horizontal hole, make a half dam of grease with your finger, and spray fluid in, etc, etc...