First of all... WHAT ENGINE do you have?? there's a few engines for corollas for 88-92
4AGE 88-89: Also known as big port has an AFM (air flow meter) you will need an AFM adapter to put an air filter on these.
4AGE 90-91: Also known as small port, has NO afm so you should be able to put something like that ram air without an adapter.
4AFE: same step as the one above.
4AF: Carburated so you can't put an Intake on it. But you can put a round K&N filter.
I don't think I missed any other engines, besides japanese 20V's and the 4AGZE, I think some 4AGZE's have AFM and some don't.
Here's a link from 4agze.com on how to make a DIY cold air intake.
http://www.4agze.com/tech/coldair.htm