There actually is a great device you can use to get tires on much easier if you don't have the hand strength to generate a lot of leverage--some tires are just really hard to get on certain rims regardless of what technique you use.

It's called the Kool Stop Tire Bead Jack:


The straight end rests on your rim. The swinging arm goes on the edge of the tire. Then you push it forward and the swinging arm pulls the edge of the tire over the rim. It's ideal for getting that really hard to move last few inches of tire over the rim.

I use it for tubeless mountain bike tires which by their nature are extremely difficult to get on a rim. But it also works fine for road bike tires! It's about 10 bucks and you can find it at a lot of retailers. I got mine from jensonUSA.com which you can find it on there for about that price if you search "bead jack."

You should still know how to get a tire on by hand, however, as it is too big to carry on the road. One nice thing to know is that "folding bead" tires get much easier to put on and take off after you mount them a couple of times. So use it to get them on there that first difficult time.