The first thing you should do when you receive an early offer is to make the other companies immediately aware of the offer. Your stock will go up markedly the moment you have been "put into play." It is simple human nature to covet what others have, and the price of membership has just gone up for those who want to join in the fight for the coveted prize. That which is difficult to obtain always holds greater value. Interested players are now required to react immediately or lose you. If they are truly interested, they will react. If they have just been stringing you along with a load of others, they will cut you free. Be prepared: you may be isolated with your lone offer. But if you are good, you may receive multiple offers.
The second thing to do is ask the company that made the initial offer for as much time as possible to make your decision. The amount of time you request may depend on the other pending offers (have an idea as to when they might be ready to respond). One week to make the decision is common and you might be able to get as much as two weeks (or more, especially if the offer is made in the first semester of your final year). But this is not the time to go out and start new contacts from scratch. It's time to wind down your search and cash in your chips.