You can use a lever to push it on. Slip the flat end of the lever under the tire bead and over the top of the rim, and just push up. You have to be careful not to pinch the tube though.
As you get more experienced at changing tires, you will learn the trick of rolling the tire on to the rim. I'm not sure I can really explain it very well, but there's a particular motion that you use with the heels of your hands that will get most tires on the rim, even if they seem tough at first.
Some tires are just tight though, especially when they're new.