I use cheap grommet pliers from Dritz, but there are some very nice machines out there, depending on your budget. Here's the Corsetmakers LJ community tag for eyelet and grommet machines. It's worth a browse-through; there are lots of different options there.

Welcome Philippa
You can post a photo and share your work if you wish

For putting the rivets and eyelets there are few different approaches, you can choose what is suitable for your needs. I use combination of special pliers for making holes and a special tool with hammer for securing the rivets in the holes. I'm planning to get an Eyelets Setting Press. The tools for setting the eyelets with a hammer comes in a package with an eyelets and it is the most affordable method.

Ive just made my first corset at art college. Id like to continue. What machine would you recommend for putting in eyelets and rivets?