It's actually very simple, although that's not quite the same as "easy"....
Call the ex-friend and arrange to come over on a night when they're not busy. If the friendship is too damaged for even that, try just dropping in when you're reasonably sure you're not interrupting anything.
Apologize profusely. Humble yourself. Berate yourself, if need be. Take all the blame for whatever went wrong and then take a little extra. Don't even try to be rational about what did and didn't go wrong. Keep talking until they stop expecting you to go on. Be sincere. This is the most important part. Truly convince yourself before setting foot in the ex-friend's presence that you're at fault, or else you'll be dead before the count of three.
Take ex-friend out to dinner, or anything else they enjoy having someone else pay for more than anything else. Stop apologizing at this point, because once you've reached this point, it makes you look like a sycophant. Be as casual as possible, except to make sure you swing a wide circle around whatever caused the problem in the first place.
Note: this is, of course, the same procedure needed to rebuild a romantic relationship in three not-so-easy steps. The difference is that the other party will have perfect retention of the original incident, and if you even look like you're going that direction again, you'll have to do this all again, and it will twice as long.
You have been warned.