I bought an RPi kit that included a wifi dongle, and that's what I use to connect it to the network. I have no monitor, mouse, or keyboard on the RPi, so I access it from my desktop computer via ssh and VNC. The RPi has ssh enabled by default, and you can connect to it via another computer on the network, like this:
ssh
pi@xxx.xxx.xxx.xxx
where xxx.xxx.xxx.xxx is the network address of your RPi. (It will probably be something like 192.168.1.101. Check your router setup to be sure.) Once you have connected to the RPi by ssh, if you don't already have the xserver (graphic mode) running, execute 'startx' (without the quotes). Then execute 'sudo apt-get install tightvncserver' (without the quotes) to install the VNC server, which I think is not enabled by default. I think I had to manually start tightvncserver but I don't remember for sure. Then connect to the RPi over the network from another computer on which you have installed a VNC viewer application. The viewer I use (in Linux Mint) is just called vncviewer, and I connect to the RPi by executing 'vncviewer xxx.xxx.xxx.xxx:1' (again, without the quotes). You now have terminal mode and graphic mode access to your RPi. (I may have left something out, but this is most of what you need to know, anyway.)