Silkies, you buy a rabbit tattoo kit online or from a farm store. There are two types, pen type and clamp type. I own and prefer the pen type, but many people swear by the clamp type. Each has pros and cons.
Anyone can tattoo their rabbit's ears with a little practice. I believe only alpha numeric symbols are OK if you wanna take em to a show table, anything else DQs them. It should be in their left ear. Any rabbit can be tattooed and these tattoos are used to denote rabbits on a pedigree. Rabbits who are not pedigreed, but have tattoos, can be used in a rabbit pedigree.
Basically a rabbit pedigree shows the pedigreed rabbit and three generations of parentage (parents, grandp's and GGPs), and all the rabbits listed on the pedigree have to be tattooed with alpha numeric symbols in their left ear, list breed, and their adult weight. That's why they have the tattoos.
Rabbits can also be tattooed in their right ear by an ARBA judge if they get registered with the ARBA. Tattoos in the right ear not done by an ARBA judge for registering DQ them too I think. Registration tattoo numbers can also be listed on a pedigree but don't have to be.