Here are some of the common steam probs I have encountered and what I had to do to fix them:
Ticket Expired- Log out and exit Steam
- Log back in again
Disconnected from Server - Client sent dropCannot get Steam to run/start updating- Logout and Exit steam
- delete the "ClientRegistry.blob" file in your Steam folder (usually "C:\Program Files\Steam\")
- Restart Steam.
Server Verification Failed- Steam is down
- When prompted start in OFFLINE mode
- Play as normal (server should let you join OK)