Depends on what the budget is. From the post's title - 1996 Corolla - I'll assume it is a 7AFE 1.8L engine (105 HP/ 117 ft.lbs). Not much you can do with that. Internals are not that strong - probably can go about 6-7 PSI before you have to build it.
Budget from $2500 and up
Turbocharging or Supercharging route (turbo would be easier). That will include the parts to get started and tuning of the system. More if you have someone else install it. For the supercharging route - you'd almost have to go custom or swap the heads from a 4AGZE to make a 7AGZE. But can be expensive due to the populatity of the donor engine. Jackson Racing and Blitz were the only ones making it for that generation of Corolla. The TRD supercharger will not work.
Budget $1000 - $2000
NOS and better intake and exhaust. Probably the best bang for the buck - but not legal everywhere. Some places will not allow transportation of NO2 without proper license to do so.
Budget less than $1000
Intake and exhaust - gut the car to make it lighter. Every bit helps - but don't huge power gains from the 7AFE - may 5-10 WHP extra.
Alternative - engine swap. Pop in a better engine. Problems, in the VA and other states that have emissions checks and vehicle inspections, the donor engine has to be the same model year or newer to be legal. That leave 1ZZFE, 2ZZGE, and JDM spec'd engines. A 1ZZFE or 2ZZGE swap will set you back about $7000 unless you find a good, used engine. JDM engines don't meet emission in all areas - may be a no go.