It will always be first come-first serve. They will think some people will not show up, the airlines will only know when too many people show up and whoever got the boarding pass will be onboard and who did not get the boarding pass will have some apologies and perhaps a hotel room depends on the airlines' policies and situation.
Therefore, only one thing that can saves you from this, show up early or get the boarding pass earlier (most airlines have the option to issue boarding passes online). That's the best effective way to make sure you will be onboard.
Most airlines allow you to get the boarding pass 24 hours before the flight (either by taking a trip to the airport counter or online), but once you get the boarding pass it is a one way thing, the ticket is not refundable anymore and you can not cancel that (unless of course it is the airlines mistake, eg. if they cancel the flight).
One more thing, you might be lucky and get upgraded if your class was overbooked and they didn't find you a seat. So if you like gambling and you do not have a problem being delayed a day or two, you can take that shot and show up little late.
As Flimzy commented, if the airlines in case of overbooking issued boarding passes more than the airplane's capacity (which happens by the way) then some people will have to deplane. How will they choose who will be rejected I do not know a standard for that. Could be by volunteering as mentioned in the comment or by some other criteria depending on the airlines. In the airlines where I work they will reject the passengers who are employees of the airlines first, I know that because I was in this situation before. I guess other airlines have similar criteria.