how is new money actually introduced in the United States? I'm aware that the fed controls the supply of money by contracting and expanding through permanent and temporary open market operations. Consisting of purchasing Treasury securities or through repos. These are sold primarily to primary dealers I  derstand but also to other organizations.

Can someone explain how the interest that is paid is set during auctions? Additionally it seems that the securities alone can not introduce money but through the interest paid on them?
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.