Your goats and sheep like to have their nails clipped too! Sheep hooves tend to grow more slowly than goat, and the sole is more sensitive on a sheep, but otherwise the technique is pretty much the same.
You will want to have a stanchion or milking stand, something that you can brace the sheep or goat against while you are trimming. Make sure you have a clean, sharp pair of hoof trimmers, and it’s a good idea to have a bottle of blood stop powder handy, just in case. Wear a thick pair of gloves on the hand that you will be using to hold the hoof steady, in case the trimmer slips. You may also want a hoof planer or a rasp, to file down the heel.
Clean the hoof carefully before trimming, and then trim away any portions of the hoof wall that has curled under. You may need to trim the toe down, as well as the dew claw on goats, and pare down the sole. Be careful cutting or filing the sole. Trim slowly and when you start to see a little pink, stop. Cutting farther will cause the hoof to bleed.
A quick tip – try trimming after a day or so of wet weather. Hooves get harder when the weather is very dry.