I have been running an auction league for almost ten years. Congrats in making the decision to switch to an auction draft system, your league will not be disappointing.
First of all we use $100 salary cap for our entire roster (14 spots). Some might suggest that is not enough but the principle of auction drafting is based more on percentages than it does on the actual salary (what % of your salary will you use for RB? QB?, etc). So as you can see it doesn't matter if you use $100 or $1000.
Everyone sits on the "roundtable" and we pick from a hat who nominates first. The team owner nominates a player and puts a price on him. At that point the feeding frenzy starts. We allow everyone and anyone (in no order) to raise the price at a min increment of $1 with no max cap. Once the bidding slows down the auctioneer (or one of us) does the traditional "going once, going twice, sold" comment. After that it goes clock wise around the table with the next nomination. The order really doesn't matter because everyone has a chance to bid on any given player.
When we started off I did everything with pen/paper/and a calculator. However, fantasy football and auction draft has evolved and there are various products out there that can help your cause. Do yourself a favor and invest in those products. We use fandraft http://www.fandraft.com/
and was a huge upgrade for our league draft and less work for me
I hook up the laptop on a big screen and the software provides all the remaining salaries, what a teams highest bid can be, players on the board, players on rosters, etc.
One last thing, DO NOT allow any trades during the draft what so ever. If you have any more questions let me know. Good Luck!