I booked a multi-city flight from SFO-IAH, then IAH-PUJ in August, with PUJ being my final destination. The SFO-IAH / IAH-PUJ lands and depart on the same day to/from IAH. It is all under the same airline (United Airlines). Since I booked it as a multi-city, will I receive all tickets for all the flights at SFO or do I receive the first flight's tickets at SFO and then the next flight's at IAH? Will my checked-in luggage be connected from SFO all the way to PUJ?
Assuming that this is all on one ticket under a single confirmation number, you should receive boarding passes for both flights when you check-in at SFO and your bags should be checked through to PUJ. When you check-in, just confirm that this is the case with the agent who tags your bags.
Note that, for the reverse trip, when you fly back into the United States from an international destination without preclearence, you'll have to clear immigration and customs at the first US port of entry rather than your final destination. There, you'll go through US immigration, claim your bags, take them through customs, and then drop them off at a designated counter (just follow the signs for connecting flights) so they can continue on to your final destination.