You just need to have them both connect to the same wireless network. Your TV either has a wireless network card built-in, or it is available as a separate device (you'll need to buy that, then). If you have a normal Ethernet cable, you can also connect the TV directly to one of the router's LAN ports, but as since you said that cable is no option, you will eventually have to go with WiFi.
Consult the TV's manual on how to connect it to your network.
Your computer should already be connected to the wireless network.
In order to stream media from your computer to the TV, you need a DLNA capable UPnP media server. There are so many of them, just choose one you like. XBMC is very popular, for example. There are also more lightweight ones such as MediaTomb. I personally use TVMobili. These are all cross-platform. Install it on your computer and add your music folder to the library.
Once you've set up the UPnP media server, your TV will be able to locate it automatically and show it under its inputs.
Note that DLNA streaming over WiFi is not very efficient. Music will play fine, but as soon as you want to stream HD movies, the performance of your network might not be sufficient to guarantee smooth playback.