Infinite Items Glitch
The Missingno Glitch allows you to stack an infinite amount of items. Put a Master Ball in the sixth slot in your pack, then talk to the man in Viridian City who shows you how to catch Pokemon. Tell him "No" and then fly immediately to Cinnabar Island. Surf up and down the right side of the island until you are attacked by Missingno (or an M with blocked out symbols). Run from the battle, and you'll have 99 Master Balls in the sixth slot of your pack. Master Balls are vital in a battle against Mewtwo.
Early Mewtwo Encounter
You'll also run into wild Pokemon on the coast that are well over Level 100 when using the Missingno Glitch. The Pokemon is determined by the position of the letters in your name. To find high-level Mewtwos, name your character DxDyDzD.
Gameshark Codes
If you have a Gameshark, input the code 01017CCF to buy Master Balls for free at the PokeStore. Input 0DA4D1B5 and Mewtwo will appear in the wild.
Non-Cheating Strategy
Mewtwo is naturally weak to Bug-type attacks, although those are relatively uncommon and he will likely defeat any Pokemon that can use them before they are able to do much damage. Mewtwo also uses the Recover technique to regain his health. Change his status to something he can't recover from, such as putting him to sleep, paralyzing him or freezing him. Articuno's Blizzard and Ice Beam techniques work well for this. Attack him until his HP is low and throw Ultra Balls until he is captured. Great Balls will work too, but not as effectively as Ultra Balls.