This is an easy task but there are a few important things you should know when learning how to change the chain and sprockets. The first thing you should always do is change the chain and sprockets at the same time. Chains stretch and sprocket teeth wear thin and lose shape. Fitting only one new item will cause it to wear out faster than it normally would as the parts won't interlock or fit together properly.
Remove the rear wheel and swap the sprockets over. All you'll need for this is an allen key and a spanner.
Line the chain up with the chain adjuster bolts wound in and take a look at where the best join will be. You don't want the chain to be too tight once it's on so you'll need a little bit of slack that you can take up with the adjuster bolts.
To remove the links you'll need a chain breaker (a specialized tool) or an angle grinder to grind away the burred end of the joining pin.
Once you've done that, connect the chain using the joining link. Make sure the clip that secures it has the rounded end facing the direction of the drive. This prevents the possibility of something snagging the clip (while riding) and tearing it off.
If you are using a solid link you'll need to get someone to hold a mallet or hammer on the backside of the link while you use a hammer and punch to roll over the ends of it (the same way the rest of the links are secured). Make sure you do this correctly otherwise it won't hold! If you haven't done this before it's probably a good idea to watch someone who has.
Now you're ready to roll! Here's some more information on how to adjust and maintain your dirt bike chain and sprockets.