The Government borrows money from the Federal Reserve Bank in order to pay for the budget deficit. The federal reserve then issues 1, 3, 5, and 10 year bonds which can be purchased by anybody in the world. The value of the bonds is determined by the trading which occurs in the bond market.
The fed's selling of bonds does not directly effect the exchange rate. The total amount of dollars in circulation is not effected by this as the sale price of the bonds covers the deficit. If people outside of the US buy these bonds then they will decrease the amount of dollars in their own country with will raise the value of the dollar there. In reality this is not often the case because a weaker dollar is often the reason why the bonds are purchased by foreigners.
Do not confuse the Federal Reserve's printing of new currency to mach the target rate with the financing of the deficit.