Hoof trimming is an important and necessary part about owning goats. This task generally needs done every 4-8 weeks depending on the goat. Most of my goats need it every 8 weeks, but I have 1 line that needs more often at about every 4 weeks. Goats will need it done more often if they are being fed grain.
All you need to trim hooves is a nice pair of sharp hoof trimmers. A stand/stanchion to hold the goat still with grain/hay to snack on can make this a nicer process and bring the goat up higher so you dont have to bend down as much. A small angle grinder or die grinder with a flap disc can be used to finish the hooves for a nice finish if you are showing them or want to make sure they are nice and level, just be careful as this option can be more dangerous.
When trimming you want to start small and gradually take off more as needed. If you see pink then you should stop as that generally means you are approaching the quick and if you knick it they will begin bleeding. For really overgrown hooves you will need to trim less, more often to get them back to normal and prevent soreness.
I start by trimming the toe, then trimming the side walls, then the heal. I like to work around the hoof gradually taking off more as I go.