Return to Balamb Garden and, assuming you're near the Centra Ruins, fly east around some mountains to reach the ocean. Keep heading east, maneuvering northish around some land as you go and cross through a strait separating the fractured, southern landmasses of Esthar from the larger, homogeneous landmass of northern Esthar. Follow the eastern coast of the southern landmass south and note there's a large desert over some cliffs - that's your immediate goal for this section.
Keep sailing south along the coast, and turn west as it turns, then continue west to spot a beach. Land on the beach and exit the garden near some mountains, cross through a narrow gap in the mountains and continue west, then east around some mountains to reach the Kashkabald Desert.
While wandering around here you can encounter Abyss Worms, Chimeras and Cactuars. You're here for Cactuars, but since they're new, we might as well cover the other two, first.
Abyss Worms aren't terribly challenging foes, capable of protect itself with Protect and Shell, physically attacking for moderate damage with its Saliva attack or hitting the entire party with Sand Shake or a body swipe, both of which deal light damage. You can Mug Magic Stones (1-19) or Windmills (all levels - can be refined into Tornado) from them and you can draw Aero (all levels), Quake (30+) and Tornado (30+). They are weak to air and water.
Chimeras are more dangerous than anything else you'll find in this desert, being capable of many nasty attacks, including Aqua Breath, Break, Stop, Thundara and the odd physical attack. You can Mug Red Fangs (all levels - can be refined into Firaga) and draw Bio (20+), Esuna, Water (all levels) and Thunder/Thundara/Thundaga. At higher levels they can get up to nearly 60,000 HP and close to max Magic. They're immune to poison and depending on which head is up top, they can absorb either thunder, water and wind. They're weak to holy damage.
Finally, onto the main event. Cactuars. These odd little cactus-memes come to life are Final Fantasy staples, usually cherished for giving out-sized rewards given the trouble involved in killing them. They're true to form in this game, as they give you a whopping 20 AP each for a pittance of EXP. You can probably grind up all your GF's abilities while only leveling once - and that's if you kept your levels low!
What's the catch, you ask? Well, their Evasion is a whopping 100%, and their Spirit is one point away from max (254/255), so even though they're not well protected by HP (they range from 200-1,400 HP) unless your Hit% is great, you might have trouble killing them. Oh, and they tend to run away from combat quickly, so you'll want Initiative or Auto-Haste to ensure you have a chance to attack, or failing that, Spd-J might help a bit, but is far from ideal.
You've got one viable solution - raise your Hit% high enough to deal with their Evasion. Squall's gunblades give him a 255% Hit%, making him your ace at cutting these cactuars down, but Selphie with her ultimate weapon also has the same 255% Hit%. Since Cactuars will only show up in pairs, so these two characters with Initiative and/or Auto-Haste should be more than sufficient for hunting. Otherwise, you can use Diablos' Hit-J to boost a character's Hit%, especially if you have Triple to junction into it, otherwise use Aura for... an okay boost to Hit%.
That's the game, then. Just run around and farm Cactuars, but avoid fighting when Cactuars appear with other foes, as their tendency to flee may result in unfortunate leveling accidents. Also, keep your HP up, as Cactuars can also use 1,000 Needles, which will deal decent damage to a single target. You should consider grinding until you have all of Tonberry's shop skills, which won't really take all that long at all.
Grind to your heart's content, then move on to the next task. If you're interested in side quests, there's still the Shumi Village and the Chocobo Forests, but if you want to continue the main story, skip ahead to Trabia Garden.
Note: While grinding in the Kashkabald Desert you may run across a UFO absconding with... a pyramid? Why do those even exist in Final Fantasy VIII? Why do UFOs exist?! Whatever the case, don't freak out - this is normal. Expected, even.