Longeing is an ART, that takes YEARS to perfect. It's about developing a vocabulary with your horse that will translate to under saddle work. It's about showing your horse how to move correctly w/o the burden of a rider.
Unfortunately, to explain it to you would require I write a book, because even just covering the basics is really just enough information to get you into trouble.
You're best to pick up a book with explanations and illustrations. I believe Reiner Klimke wrote a book on longeing and that would be one of your best resources.
You'll need proper equipment to start: longeing cavesson, proper length longeline (at least 30ft), and a longeing whip.
You'll have to learn how to hold the longeline, how to cue different things with the longeline, what the whip cues are, where to position your body for various cues and so on...
Then there is the verbal cues that must be learned and applied correctly, and finally how you 'use' your body to affect the horse. How opening and closing the hips affects the horse, how to collect yourself to collect the horse and so on.
Finally, longeing 'may' be done on a circle, but a good trainer will longe on straight lines, serpentines, diagonals, as well as circles of varying sizes depending on what is being asked of the horse.
So you see, it's rather involved and gets more involved when you begin to long line.