There are two different kinds of recovery involved when your spouse has an affair:
There's Personal Recovery - regardless of whether the marriage survives
There's Marital Recovery - where there's a rebuilding of the marriage.

For instance:

Some people who stay married DO personally recover - and some who get a divorce DO personally recover.

Some people who stay married DON'T personally recover - and some who get a divorce DON'T personally recover.

So here are some keys steps involved in Personal Recovery:

Accepting the fact that it happened (no more "if only..." or "why me?")

Understanding the complex reasons for affairs (not just "personal failure").

Deliberately focusing on dealing with it and talking openly about what happened.

Allowing time to heal.

Believing it's possible to recover.

For more understanding about why affairs happen and how to recover, see:
The Monogamy Myth (A Personal Handbook for Recovering from Affairs)
Recovering from Affairs (a Handbook for Couples).