The 3 main methods for me are:

When Penelo leaves your party after Giza Plains, get as many phoenix downs as possible. Go to the Dalmasca Westersand, reduce Vaan's HP to under 10% and take the north exit. Dustias will now appear. Just use a phoenix down to get over 1000 exp, very good for that early. If you want to chain them, you must get out of that area before the LP and EXP are displayed.

After you beat Judge Bergen, talk to the acolyte outside to get some item. Go to the Stilshrine of Miriam and to the back of the entrance room. Use the item to go to a secret area. Go through the door and you will have to fight an optional esper. It's not tough, and when you beat it, undead monsters appear in that room where you can gain 300-500 exp per monster (using 3 ally party). These respawn very quickly with little action needed.

Undoubtedly the best levelling up spot in the game, but requires quite a high level (65+ is recommended). It also requires you to have killed at least 10 espers. Go to Jahara village and speak to the Geomancer (second screen). Now go to Henne Mines and use the gate to take a big shortcut to where you fought the boss. Go forward (east) to go into the secret area on Henne Mines. The place is covered with abysteels with around 20k HP. Use sleep(ga) to put them asleep and then curaja to kill them. Keep going until you reach another gateswitch room (like the room where the jellies drop in the storyline). Press the switch to get 10 abysteels to drop (with about 10 more following eventually). These give over 3000 exp each (with 3 ally party) and thats WITHOUT embroidered tippets. Mulitiply that by 20 to find you get about 60000 exp per round (120k with ETs). The quickest way of respawning them is to take the only exit available and taking the first left and then go back. With practice, you can get millions of exp per hour.