Go to Lunch
If you're lucky, your co-workers, be they consultants or employees, will ask you to go to lunch on your first day as a consultant. Under no circumstances should you refuse. If you brought lunch, toss it. If you're not interested in the cuisine, suck it up. One of your primary goals when starting a contract is to fit in with the team and going to lunch is an easy way to start that process.
Once you're at lunch, try to avoid doing anything that will decrease your chances of being invited again. Just use a little common sense. For example, if you end up in the company cafeteria, don't complain about the lack of options or extol the virtues of a previous company's cafeteria.
Also, let your co-workers decide when to head back to work and don't look at your watch. Yes you may take a hit on your billable time that day, but it's a worthwhile investment.
Lastly, if on following days you are not invited to lunch, take the initiative to invite yourself. A minute or two before the usual lunch time, politely ask someone if they'll be heading to the cafeteria today and then tag along.