There are two ways to get the Master Summon Materia (which lets you cast any summon in the game).
Method 1: Master all 16 summons in the game.
This is likely the quickest way, but there are pitfalls.
5 of the Summon Materia are missable (Ifrit, Ramuh, Bahamut, NEO Bahamut and Phoenix). So if you're at a point in the game where you've missed one or more of these, you're going to either have to start over, or use method 2.
The fastest way to master materia is covered in this video (for which I claim no credit but it's the one I used)
Just equip the materia you want to master, and go the location in the video and get grinding.
Method 2: Defeat Emerald Weapon and take the Earth Harp to the traveller in Kalm Village, he will then give you a Master Summon, a Master Command and a Master Magic Materia.
There are several guides (including one from yours truly) on this site to defeat Emerald Weapon
Good Luck