First, make sure you and the other owners have enough time. Lots of time - auctions are a lot of fun, but they take quite a while, and you don't want to have to rush.
Then, decide on a salary cap available to each team. $260 is traditional, but there's nothing wrong with using other amounts.
Next, determine the order in which owners will be able to throw out players' names. If you're all meeting in the same place, randomly determine the starting owner, and then go around the table you're sitting at. If you're meeting in a chatroom or via conference call, you'll have to randomly determine the entire order.
(Note: if you're using a chatroom, you'll need to figure out a contingency plan in case an owner's software crashes and he or she is offline for a time.)
Then, the first owner names a player to be bid on, as well as an opening bid, for instance: Pedro Martinez at $20. Then the bidding begins, with at least a $1 price hike per raise. You can have somebody act as auctioneer for this, or have the player who named the player being bid on handle things like saying, "going, going... gone." Somebody should also keep a master list of players bought and money left for each team. After a player has been bought, the next owner names a player, and bidding begins again. Note that there won't always be raises; sometimes, the opening bid will stick.
Each team needs to fill an entire roster with the available money. Thus, if you have four roster spots to fill and $18 left, you couldn't bid more than $15 on a single player, since you need to have $1 left for each roster spot. When all teams have filled their rosters, you're set.
Anyway, that's the basics. Does that help?