My boyfriend got tested also when he was really young and he says that it was awful….They basically do it the same way as they would adults. Test a small area of skin with different things, and wait. They don't have to stay still I don't think.

Scratch test on the back. It's little plastic needle like things that they ***** the baby's back with. The allergens are on the Htip and need to penetrate skin.
It will be painful, but it may save your baby's life, so you have to do it.
You will get to hold the baby in your arms while they do it (if they don't do it that way, find another allergist).
Be prepared to comfort him/her and maybe have a square of chocolate of other favorite snack to help calm them down.
The baby will have to be shirtless for 20 minutes after they ***** him/her and there can be no touching of the area until the test is complete.
I gave my baby a lollipop and a sticker and he got to run around the office flirting with the nurses.
If there are any horrible reactions, the staff is fully prepared to deal with it. More so that any other doctor's office.The likelihood of a severe reaction is slim. The scratch test will reveal severe allergies with only some swelling.
During the test you may feel bad that you did it to your baby, but after you get the results, you'll know that it was the best thing, and should not have been avoided for any reason.
Good luck, and I hope your baby is clear of allergies. They can be life altering.