I don't know if my bird enjoys being in his carrier but he definitely does tolerate it. The breeder he came from crate trained him before I got him. Sometimes he doesn't seem to want to go into it but he usually will. I would let him see me put veggies or nuts in the back so he would go in easily when he was starting to be hesitant about going in. Now he will usually go right in and I'll put veggies or berries in it for the trip. It's just a small animal carrier with a perch inside.
It's like the one below.
One easy way to train your bird to go into the carrier is to have it open to them and to put their favorite treat in the front of it. Let them take their time and get curious enough to take the treat. Once it's comfortable sticking it's head into the carrier to get the treat start to move it further and further back until it is comfortable walking completely into the carrier. Once it's comfortable walking into the carrier you can start closing the door for a second. Then close the door for increasing amounts of time. Make sure there is enough of the treat that it's more concerned about eating then being closed in the carrier.
There are different ways that you can train your bird to be comfortable in a carrier, you can also use clicker training. Use whatever motivates your bird and make sure you pay attention to it's body language and go as slow as your bird needs you to.
I think the biggest thing about crate/carrier training is to keep them trained. If you have a well trained bird that enjoys the carrier but you only put it in the carrier to go to the vet you'll quickly have a bird that will refuse to go into the carrier. Make sure you take it to fun places more than to places they don't like. 9 times out of 10 we're going camping when my bird is in his carrier so he doesn't associate going in it with bad experiences.