You constantly place your bids on the NFT that you like to purchase. During the bid time, you can continuously place a higher bid. At the end of the auction, the top X highest bids will receive the NFT. You can actively see who is the highest bidder.
In silent auctions, there will be a small time window (often 10 minutes) to place a bid on an NFT, which usually has multiple editions available. The bids are not revealed until the end, at which point all the NFTs are assigned to bidders in the order of highest to lowest bid until all are allocated. These can sometimes be profitable for a short-term flip if you can buy one at the low end of the bidding range. However it can be risky given the possibility of overpaying. During Silent auctions, you cannot actively see who is the highest bidder.
Once the sale goes live, you are able to buy an unlimited amount of NFTs until the sale ends.
Before the drop, there is a possibility that there is a waitlist you will be able to join to purchase the NFT. For Limited Edition drops, once the sale is live the NFTs will be sold in numerical order based on your place on the waitlist. If there is no waitlist it will be sold on a first come first serve basis.
The sale will be complete when all of the NFTs are sold out or the drop duration ends.