I generally use Mountboard. This is normally a rigid coloured card from a craft or art shop, can sometimes be found in stationers too.
I will buy an oversized frame, and cut the mountboard to size to fit the frame, i will also cut the centre of the mountboard out to leave around 1-2 inches border around the edge. This also needs to be at least half an inch smaller than the actual painting (always best to have a good border around the painting too to help with the mounting.)
I will fix the painting from the rear of the mountboard so when you turn it the right way round you have a nice trimmed border with the mountboard, fit it in the frame and jobs done
I hope this makes sense, will also make a good short tutorial so ill add it in shortly