Well, I learned mole trapping the modern way, watching youtube. I have been mole free for a couple of years now, but for sure there is a learning curve. I used a claw type trap which I thought worked very well for my sandy soil and it was easy to use. It uses the moles natural instinct to tunnel under objects to trigger the pressure plate. I don't believe it's absolutely necessary for moles, but I always use gloves when handling traps and I rub the traps in soil before use to get rid of any human scent.
Here is one of the videos I watched, but search around and look at others as well, to see what suits you best. It can take a while before you get your first catch, but don't give up. I thought that I couldn't get it to work in the beginning, but it got much easier over time. The main problem for me was to find an active tunnel. Sometimes you need to move the traps around before you find a good spot. There are however videos you can watch to learn that as well. Just look around a bit and be patient.
The brand I used was different from the one in the video, but it always killed the mole quickly and cleanly. I would personally not try to relocate an animal as that can cause long suffering and starvation death.