You need a wireless access point and nothing else if you already have a LAN set up and you desire no extra functionality besides wireless access.
I am assuming you already have a router to share the internet connection. Seems that many people buy an additional router with wireless and then have to go through hoops to get them working.
A decent AP would cost between $100-$200. Make sure you get one from a proper manufacturer. If you are not sure whether a brand is respectable, come ask here. Getting it from the same company that made your router and/or wireless adapter(s) would be very good.
You could also get away with any old PC running Linux operating as access point. It would take lots of tinkering to get such a setup running though.