How do you add fluid to the transfer case?

The transfer case has 2 plugs, an upper and a lower. The upper is the "fill" and the lower is to drain. If you are going to go there, just drain and refill with all new fluid. The plugs usually take a 3/8" or a 1/2" ratchet to open. You will see the female square holes

Thanks for the reply. I think it has solved my problem.

Yes... But the '99 blazer takes a 10mm allen socket for both.