Grips and handlebar tape were created to make sure that cyclists don't have to grip the metal of their handlebars. Unfortunately, these things wear out, but the good news is that they're really easy to replace.
Before installing new grips, the old ones have to be taken off the bike. If you're not planning on saving or re-using them (a good idea if they're threadbare or already falling apart), just take a large knife and cut them off.
To install the new grips, get the grip and handlebar wet. This is very important as it makes it easier to get the grip on the handlebar. The grip and whatnot don't need to be dripping wet but wet enough that it's obvious they're wet and will be obvious when they dry.
Next, slip the grip onto the handlebar all in one motion. If it gets stuck, you can use more water, compressed air, or a hammer. It shouldn't get stuck but it might.
The big thing is that you have to wait for the grip to dry. Don't ride the bike until the grip is dry and the seal is tight on the handlebar.
When installing foam grips on downward facing handlebars, water alone won't be enough to get the grip on. Soap is definitely need. When selecting a soap, make sure it's a soap that will dry.