Bots will do the following if they have a waypoint file for the level. (not all the behavior is listed, but it should give you an idea)

Bots will roam about looking for:
- Flags
- Health
- Ammo
- Armor
- Enemy's
- Dropped items (flags/ammo etc.)
- Other items (switches etc.)
- And depending on their class they will look for
-- Sniper points
-- Sentry gun build points/guard points

If a bot sees a friendly sentry gun, it will drop spare ammo for the engineer.

When the bot has a flag/key it will attempt to capture it, only engaging the enemy occasionally.

If the bots health/ammo is low, it will look for some.

Each class has slightly different behavior.
Scouts will usually go mainly for flags/keys without engaging the enemy (just running past the enemy)
spy's will disguise them selves

Bots in combat will do the following:
- Jump (rarely)
- Throw grenades sometimes(if close enough/far enough away)
- If they can no longer see the enemy, they will attempt to follow them from where they saw them last.
- Spy's will attempt to backstab (if disguised)
- If a bot sees an enemy sentry gun, they will attempt to kill it without being shot.

Bots will sometimes inform you of what they are doing/attempting to do.