The Treasury auction process is described here: Treasury Direct
Bidders can either enter competitive or non-competitive bids. Non-competitive bids are limited in size; the price is set by the competitive bids, which generally come from Primary Dealers (that are obliged to bid).
As a simplified example of the bidding process, assume that the government announces an auction for $2 million in 30-year bonds. (Note that this example ignores bidding size limits.)
There are three bids:
- a bid for \$1 million at 4% from A
- a bid for \$1 million at 4.25% from B
- a bid for \$1 million at 4.50% from C.
The government looks at the bids (starting with the lowest yields) until the amounts cover the amount to be issued. The highest winning bid yield is used for all. In this case, that means that A and B get filled with a $1 million in bonds at 4.25%, and C gets nothing.
The connection to money is somewhat complicated. The issuance of the bonds reduces the money supply - the bidders have to pay for the bond. The coupon and principal payments will increase the money supply.