Yes, bidding at an auction is a game of wits, and has some strategy to it. Here are some methods I have seen, and some I have used to be a successful bidder.
Numero uno!! Set a price limit before bidding - figure any extras like premiums, and taxes into that amount and lower bid accordingly. Do not get caught up in a bidding war from auction fever.
Pay attention to who is bidding, some less than reputable auctioneers use shills to up the price. Positioning yourself properly in the crowd can help spot the bidders.
Be careful who you talk to, and talk around, but that does not mean don't listen to what others may be saying.
Now, bidding styles;
Some auctioneers start high, then keep dropping the bid until someone jumps in. Many times on an item like this the price will go right back up to the starting point in a hurry. I have hit the starting bid right away on items to let the lowballers know I was serious, and they don't even jump in. You may not pay the lowest it might have gone for, but you will get it in your price range. This is where gaging the crowd comes in. How many are hanging around and eyeballing the anvil? 1, or a dozen? Do they look like they can drop how much you can, or way more than you?
Sometimes I have yelled out a bid quite a bit higher than the auctioneer is asking for to get it going. This has usually been when the auctioneer is starting low on a popular item. They may be asking for $50, $100 etc, and I would just yell out $400 as an example. Many times it goes well past my initial bid, sometimes I get it at that bid, but it shows you are serious, and it also gets things moving along.
I won my 1967 M-715 at a DRMO auction by being the first paddle up, and just holding it up the whole time, never dropping it down. I wore out three competitors. The final bid was to me for $1,000, and that was my limit. Fortunately, they dropped out, as one more hit and it would have been theirs. My heart was beating a hundred miles an hour.
Some wait for the second going (going once, going twice, all in all done? SOLD!) before hitting it again. When I have someone doing this I hit it back as fast as I can. Just holding the paddle up constantly also helps to keep someone else from jumping in at your limit if you lag. You know what your limit is, so don't be afraid to run it up to it.
Don't dilly dally. Some auctioneers are fast to close , and quick with the gavel if they have a lot of items to work through. Some will close fast if it is a friend bidding, so be fast on paddle.
Pay attention to what lot is being sold! Don't be the doofuss that bids on the wrong item. Also some auctioneers will go out of order. I have seen this a few times. They go until a certain time, then jump to the big ticket items that most came for. Don't miss a purchase because you were munching on a hot dog, or in the can. Also make sure the auctioneer, or minions actually see you. This gets important if your competitor is inline with you. Don't be afraid to ask what bidder number is the high bid if they do not say. I have been to a ton of auctions, some run very well, others no so well. It is up to you to pay attention as to what is going on.
I have taken lunches, and drinks to big auctions. Stay hydrated.
Be careful of round robin bidding. This is when there are three or more bidding on the same item and the auctioneer is going in an order. Be figuring out what it will be when they get to you, and if it will put you over your limit. If so, you can always just jump the bid to your limit and hope for the best.
Multiple like items. I was at an auction where I wanted a welder. It was a big shop with a line of welders, many were the same make and model. This is where you need to pay attention. The Millers and Lincolns were going high, but when they got to the Linde UCC-305's hardly anyone bid. I dropped out and let the guy in front of me win the bid at $250 as I guessed he would not want all three at that same price. He picked the one he wanted that had a few hundred feet of lead draped over it, and I was ready with my paddle when they asked if anyone else wanted one at that price...bam! I chose the one with the radiator and ended up with an absolute fantastic TIG welder for a great price. The high bidder ended up buying the last one for $140 for parts. Some auctioneers will make you choose in numerical order, others let you pick and choose. Pay attention! I have seen this go may ways. I have seen the high bidder take all of them at the price he bid, and I have seen the first one go high, and the last one go dirt cheap after everyone got one. This is where gaging the crowd comes in, and seeing who is bidding on what. 15 items and 10 active bidders? May be worth just hanging out and see what the last ones go for instead of just running the price up. Everyone gets a good deal then.
I love a good auction, and miss going to the DRMO's at the local military bases. Unfortunately they have all gone online now. I knew who the scrap dealers were, the kitchen equipment guys, medical equipment purchasers, etc.. Most of my machine shop equipment came from one auctioneer, one of the best I have ever had the pleasure to bid with, Very well run operation.
Good luck with the anvil!