You obtain the 1st Mystile in the game from a treasure chest after fighting Proud Clod in the return to Midgar; that's simple enough.
In order to ensure you get both the 2nd and 3rd ones, you have to juggle around a bit in the N. Cave on your descent.
When your party first splits, send Tifa down the right path and go down the left path yourself. When you reach the bottom of the Crater, rather than talking to any of your party members, head straight back up the Crater again. When you reach the cut-off point where your party had first split, this time take the right path yourself.
You will find the 2nd Mystile in a chest along the way on the right path. Proceed to the bottom of the Crater again. This time talk to Tifa. She will give you the 3rd Mystile. It's a bit of a cheat/glitch, but it's very good to have 3 of the best Armor in the game: it means you can equip a Mystile on everyone in a 3 character party.
You can use variations of this glitch to get teammates to give you other Items. It can be handy getting 2 Mega Alls for example, but you could always just get more by mastering them. It is also possible to obtain 3 of the Imperial Guard Armor by picking up 2 in the N. Cave and getting one off the boss in the final Fort Condor battle (you must fight him with your level high enough), but the Imperial Guard Armor isn't really great - high Defence % and Magic Defence % tend to be more effective than high Defence and Magic Defence.
I recommend sticking to Mystiles, Ziedrichs, Escort Guards, Minerva Bands, and possibly Wizard Bracelets for extra Materia slots or the Aegis Armlet. The Aegis Armlet is a bit like a mini Mystile as it also has decent Defence % and Magic Defence % - it's often overlooked in FF7.
For full details on the above mentioned Armor, including where to obtain them, visit my Armor List page.