Disneyland, right? Not WDW.
We're talking the Legacy fastpass system here. For the attractions that offer Fastpass, there are machines that dispense a ticket for each person. You use your entry ticket to Disneyland to claim the FP. Each entry ticket, assuming that it's been activated by the owner of the ticket for the day through the turnstiles (i.e., with fingerprints), will provide you with one FP. Disney do issue the FP for free and they have worked out how many they can distribute in a hour/day so as to keep the queues going. The only FP machines that might have a queue will be RSR. That's because everyone heads there first when DCA opens up and RSR is such a popular ride that the FPs for the day are distributed very quickly if you don't get one early. Aside from RSR, I don't think I've waited any more than a minute to claim FP for the others at DLR.
When you get the FP, it will have a return window printed on it. Think about it as someone 'queueing' for you and then you coming back to your spot in the line. That's what the FP will do for you. You'll need to come back to the attraction between that time window in order to claim your spot. If you're too early, you haven't hit the front of the queue. If you're too late, you've missed the front of the queue. When your time window opens up, head to the FP entry; rather than stand-by to get the 'expedited' entry. For some rides, you might still have to wait; but usually it is less time than waiting stand by. The FP entry route will take you towards the front of the loading area for the attraction.
Disney implements 'rules' for the distribution of the FP and how many you can hold at the one time.
Once you've gotten the first FP, you can only claim a second FP either at the start time of your first FP window; or after 2 hours....whichever comes first. Essentially, you would need to work out which rides you want to go on and send a FP runner ahead to collect the FP tickets when your window is opened.
There are a few exceptions to the time rules of collecting FP. Some of the attractions that issue FP are not linked to the "mass" e.g., the FP distributed for WoC and I think the FP distributed for RSR might not be tied in to the central system. There used to be a couple of others as well but I think Disney might have linked them all to the central system now. You can either google or someone else can correct me if I'm wrong.
It used to be the parks at DLR were also on separate systems. So that meant that if you got a FP at DL and then moved to DCA, you could collect another FP there irrespective of the time rules (assuming that you had a park hopper ticket). Not sure if this is still the case or not.
There is a whole planning strategy around how, when, why you would collect a FP or go stand-by. That is a whole 'nother essay.
Hope this helps.