Bid what you want to pay for the item if you are trying to squeeze another bid in you didn't put your max bid in.
This doesn't work well.
You should put your max bid in at the last second.
You assume everyone else puts their max bid in ahead of time. You also assume people are rational. Sometimes people really want an item and think "I'll only pay 5M for that. Max." They bid 5M, lead the auction, then get outbid by someone at 5.5M. Sometimes, the first person will then bid 6M, despite the fact that their "max" was 5M.
If you are the 5.5M bidder, you'll get the item if you enter your bid with 2 seconds left, but not if you enter your bid with 2 hours left.
Let's say there is something I like on the AH. Let's say they are boots that are sitting at 1M, no buyout, and I'm willing to drop ~12M on them. Here's what I do:
1. Bid incrementally, just so it shows up in my auctions. They are now at 1.1M or so.
2. Set a timer for ~10 minutes before the auction ends.
3. ...
4. When the timer goes off, load up the AH, and check the bid. If it's below my max, I'll refresh the auction every second or two until it goes from 8 minutes to 7 minutes, then start my timer from 7 minutes
5. Open the bid window, enter 12,045,246
6. Wait until 2 seconds left, press enter
If I bid higher than anyone else, I win. If not, I don't. If someone was happy with an 8M bid, sees that they got outbid and now wants to up their bid, they don't have time to do it.