I agree with all of the above. Just to clarify for the OP ....
If you have 5 people in your party, each of you has his/her own card. If you are all hoping to ride, say, Space Mountain together, each of the 5 cards has to pass through the FASTPASS machine, one at a time. You can't get 5 FPs from one card. However, you can have one person from your party gather all five cards and go over and get the FPs while everyone else is doing something else. In fact, this is usually easier and quicker than having a gaggle of 5 people hanging around the machine.
FASTPASS attractions tend to have about 4-6 FP machines, so there's usually little or no wait to actually obtain FPs.
Also, just in case you were going to ask eventually, a FP machine will only give a FP out to a card that has been used to gain park admission that day. We've seen this question asked before. In other words, let's say you're staying at Grand Floridian, which is right next to Magic Kingdom. You can't have one person gather the cards from the rest of the sleepy-heads and go into MK himself/herself to get FPs for everyone. The Almighty Disney computer database will know that only that one person gained admission to the park so far (that one card was the only one inserted into an entrance turnstile), so no FPs will be issued for any of the other 4 cards inserted into the FP machine.