Okay, so you are right that you need to wire and prune it, however, if I were you the first thing I would do is repot it. By repotting it and trimming the roots, you affect what happens to the branch system. A bonsai with lots of small roots will have lots of small branches and leaves above.
First of all you need a shallow dish with holes in it to be your bonsai pot. You can get these very cheaply on amazon and they will be just fine. Then you need to make sure that you have good quality bonsai soil. You can either buy this premixed or mix it yourself, depending on what you can find. You will also need some gravel, wire, and plastic mesh.
When you have all of these things you can start the repotting process. First, cut out small squares of the mesh and place over the drainage holes of your pot with the wire. This will stop soil being washed out of the holes. Attach long pieces of wire to the pot using the drainage holes. You will use these pieces of wire to hold the tree in place. Then add about a centimetre of gravel to the bottom of the pot to aid drainage. Next add the soil to about half way up the pot.
Now turn your attention to the tree. Take it out of the old pot and use a chopstick or similar object to rake through the root mass. This will untangle the roots and remove the old, unwanted soil. Once around a third of the soil has been removed, examine the roots. There should be a thick root in the middle of the root mass. This is the tap root and is used to hold the tree into the ground. As this is a bonsai, there is no need for the tap root and it should be cut off, using sterilised pruning scissors. Any other thick roots should also be removed. Now you want to trim the root mass so that it will fit into your new pot. Trimming the roots will encourage, smaller, finer roots to grow which is exactly what we want.
Now you need to carefully place your tree in the centre of the pot and use the wires to secure it. Then fill the pot with the bonsai soil. Use a chopstick to make sure that all of the empty space between the roots is filled. There should be no air pockets as this is very bad for the tree. You may want to cover the tip soil with gravel, but that is your personal choice and is simply for aesthetic purposes. You should then sit your tree in a tub/sink of water for ten minutes to give it a good soak.
Repotting will be a great ordeal for your tree and it should be left to recover. It may experience leaf loss but this is normal. You should not fertilise your tree or do anything else to it that could cause stress. Later you can prune and wire your tree to the style that suits you but in the mean time just let it settle down.
Michael was right about this being in the wrong section so next time remember to choose the one that is relevant to your topic so you can get more replies
I hope all goes well