Both tethering and wifi wireless connection to your mobile phone should be straight forward. There are many ways to get it working, but the easiest one is to install
NetworkManager. It is actually an applet, available in most distros, and should run on any window manager. If you are going to use tethering, connection should be as easy as plugging the usb cable (your laptop will see it as a normal cable internet connection, and NetworkManager should connect automatically.) If you are going to use wifi, all you need to do is to configure your wifi connection in the NetworkManager (it's pretty easy, basically you have to give the password you've set on the phone.)
I had issues to get wifi or tethering working on my phone though. Depending on the phone, it might not be set to work out-of-the-box. If I were you, I would install NetworkManager before going to need the phone connection, and give it a try now. That's because you might need to search on the Internet how to set up your phone for this. Actually, it's more likely you will have issues making the phone working for that, than having issues with the Linux laptop itself.