Honestly, I don't mount or dismount tires anymore although I did a couple of junk wheels this summer so I could build a vise stand with a old wheel and a sawed off driveshaft.. but that's another story. I got into doing this back when my first set of "mag" wheels got screwed up by a "pro" in 1972.
All I've ever used was an old tire spoon that probably came out of a 30's or 40's Ford and a cheap balancer I bought from JC Whitney 30 years ago. A can of silicone spray and that's it.
Mounting tires is easy, dismounting them is a lot harder.
To mount a tire, first look at the profile of the wheel. The side that is closer to the "drop" where the wheel is smaller in diameter. The side that is closer to the drop is the side you want to start from.
Spray the bead and wheel with silicone spray and put the tire on the wheel at about a 30* angle and push. The bead nearest to you needs to fall into that drop. If you are lucky, one side of the tire just popped on. (It really helps to be a big guy) If it didn't pop on, you'll need to take the tire spoon and pry the far edge of the tire over the wheel. That's the easy side.
The other side takes a little more work. Push the tire down to the bead nearest you into the drop and push down on the rest of the tire. I sometimes stand on the tire in that area to keep the bead down. Push the rest of the tire down and around the wheel. When you get it as far as it will go, take your tire spoon and pry the bead over the wheel. Blow the tire up and you're done... wipe the sweat off and take a sip of your beer.
Of course.. if the beads won't seat and the tire won't inflate.. there is the starting fluid trick.. While I've done that, its not for the faint of heart.
http://www.youtube.com/watch?v=TzbgyRrQybQ&feature=related
Dismounting them is another story. First you have to break the bead.
Ever wonder why the base of your bumper jack has a slight curve in the side? That's so you can brake the tire bead. You'll find that in older (50's) Chrysler Service Manuals. Place the tire and wheel flat under the bumper of your favorite old Mopar and place the jack base on top of the tire with the curved area close to the tire bead. Jack the car up and the tire bead will pop off.
You pretty much reverse what you did mounting the tire... or I've taken the sawzall (one of my favorite tools) and cut the tire up leaving the tire beads. You can then cut the beads with a bolt cutter.
All that said, there's the Harbor Freight tire mounting tool for $50. I would buy one of those and mount it to a pallet like the guy in these videos.
http://www.youtube.com/watch?v=_LAABOgXU1s&feature=related
http://www.youtube.com/watch?v=qbfXfnv5ZFU&feature=related
The last tires I mounted were for the Corvette so we could go autocrossing. I scored some nice used wheels (IIRC, 17x10) and some "take offs" from a SCCA sportsman class car. My oldest son said something about having them mounted... and I had to show him the old man still had it.....