Just wanted to put in my two cents....maybe it'll help.
First off....gotta have "real" tire irons. The BIGGER the better. I'm using Magnum 15" irons. They're CHEAP!! About $8.00 each. Got all the right curves in all the right places. Make the whole job WAY easier.
Now...like Dave said...make sure you lube the bead of the new tire. I personally set my wheel on the floor on a hunk of scrap carpet . I kneel with the rim in front of me. I put one side of the tire on the rim . I then stuff my DEFLATED tube in the tire and fasten the valve stem lock nut. Keep in mind, the rim lock and rubber rim band never came off the rim and are already in position when putting the new tire on.
Okay... you're almost home. Here's the trick. When you're trying to get the last side of the tire on , MAKE SURE that the side you already put on does NOT seat against the far side of the rim yet. It must stay in the deepest center part of the rim. You know...the smallest diameter part of the rim. Now I start to work my way around the rim with the irons. I'll use my knees to hold the rim from moving by kneeling on a portion of tire already with both sides on the rim. Make sure to have your bead lube on hand if the bead starts to get dry. If it starts to get hard to pry the tire on at any point...double check the tire position on the rim...remember, CENTER. You should be able to work your irons around the rim with very little effort. Even at the last couple of inches of tire, it shouldn't require you to fight it. If it does, then you're doing something wrong.
After the tire is completely on the rim, I inflate the tube to about 40-50 psi. Just do this to seat the tire and make sure the tube straightens out in the tire. Now drop back to your normal tire pressure and tighten your rim lock. Do not tighten the rim lock before you inflate the tire. You'll end up with the tire out of round on the rim.
Hope this is clear enough to understand. It's really the kinda thing that is passed along better visually.
Also a trick for getting tire off ....if you need it just ask.
Now I can see why they say a picture is worth a thousand words.
GOOD LUCK!!
P.S. If you like , you can email me and I'll give you my phone number. I can probably explain it better over the phone.:D