Sounds like the ranges you are looking at run what are called 3x600 matches - three stages @ 600yds.
At sign in or shortly there after, the match director will give you a score card with a target number and relay number as Eric described. Usually there will be a short shooter's meeting / safety brief, after which people go to their assigned places. Relay #1 starts bringing their stuff to the line (but not their guns, yet) and setting up their shooting mats, range bag, rests, etc. on the spot assigned for their target. Relay #2 sets up a folding chair or stool behind and slightly off to the side of the shooter on their firing point, so they can score for the shooter. Relay #3 heads to the target pits to set up the targets and make everything ready.
Relay #1 shoots, then there is a pit change - Relay #3 comes out, Relay #1 heads down to the pits. Relay #2 shoots, Relay #3 scores. Then they swap, Relay #3 shoots, Relay #2 scores. Relay #2 shoots again, and #3 scores. Another pit change, and Relay #2 heads to the pits, #1 comes out. #3 shoots, #1 scores, then #1 shoots, #3 scores. #3 shoots one more time, then another pit change and #3 heads to the pits and #1 sets up to shoot, and #2 comes out and scores. Finally, #2 shoots and #1 scores.
Relay #1 shoots first, and often gets the best (mildest) conditions of the day. Relay #3 starts out and finishes in the pits, and has to get the targets out and put them away. Traditionally #3 is the newer / lower ranked shooters, and #1 is the more experienced / higher ranked shooters (i.e. rank has some privileges). Depending on how the squadding works out, that may or may not happen at a particular club, but some places do it that way so the more experienced shooters - the ones most likely to be vying for Match Winner - shoot together on the same relay under the same conditions all day. Other places spread the experienced people out across the relays to help herd the new shooters around and show them the ropes (how to pull and score targets, for example).
If the above is confusing, don't worry. Talk to the match director before the match, explain you are a new shooter, and they will likely have someone look after you. If all else fails, follow the other shooters on your relay - if you look around and they are all headed for the pits, you probably should be also
