If the module is loaded, are you seeing an interface pop up under ifconfig? If you have something listed under there corresponding to the USB device, then you should be good.
If you need to use a different driver, then yes you need to compile it against your kernel (unless the driver you downloaded was pre-made for your distribution/release/kernel). You would need to make sure your built environment is sane, make sure you have the proper kernel source, and then do ./configure && make in the driver's source directory. Then it is a matter of installing it into the /lib/modules directory for the currently running kernel.
The driver should have come with a README that explains this in more detail, but it really isn't that difficult assuming you have the prerequisite setup.