(First, if you have an automatic, stop worrying about making it faster and swap in a T5.)
Here are your choices.
TURBO:
You are gonna want to find a donor car. The easiest one to find is a Thunderbird Turbocoupe. If you get an '87 or '88 model, you'll want to swap out the tiny IHI for a T3. Pull the motor and trans out, take it apart (the motor), and clean it up. Gather the remaining wanted/needed parts to put it in (i.e. new gaskets, boost controller, blow off valve, front-mount intercooler and ducting, 3" exhaust, LA2/LA3 computer or LB2/LB3 for automatics, 35lb (brown top) injectors, big Vane Air Meter (VAM), and any other modifications you'll want). Put it back together, pull out your old motor, and drop in the new motor. Get it running, and enjoy.
That is just the simpllified process. In a stock configuration, running ~19lbs boost, you should make around 230hp. Mileage may vary.
Good step-by-step instructions can be found here:
http://24.91.96.177/stinger/turboswaphowto.html (Stinger's website)
NATURALLY ASPIRATED:
This is a much more challenging route. Pull out your old motor, and take it apart. Get the bare block vatted. Get high-compression forged pistons, and stronger rods. Shave the head a bit. Get a better n/a cam (the A237 is a popular one). Gather any other mods you'll want (bigger throttle body, mass air swap, custom-burn chip, 2.5" full exhaust, ported head, ported intake manifold, etc.). Put it all back together, and drop it back in. Get it running.
This is also a simplified prcoess. This should net you ~140-170 total hp, depending on how extreme you take the cam, compression, porting, etc.
NITROUS:
Same as n/a. I would guess a 75-100 shot should be OK with forged pistons on the street w/ pump gas.
Be sure to check out the Tech Articles Thread at the top of the 2.3L forum page.
Some other good links:
http://gt350r.stangnet.com/index.html
http://www.40bob.com/index.html
http://www.wheelspin.net/projectcars/87coupe/87coupe.html
http://www.turboford.org/