The Fed sets the overnight interest rate that is the base of the whole yield curve. The Federal Funds Rate. This is what they have recently dropped and what Trump wants them to drop to zero.

Government bonds (and corporate bonds) have a coupon rate that is set at the time of issue. At the time of issue, the bond’s rate and its yield are essentially equal. So, you might issue a ten year note with a coupon rate of 2.25% and a price of par (100-00). It’s yield to maturity would basically be 2.25% at that time (+/- some minor adjustments related to when it pays its coupons, etc). Over time, the market’s view of economic prospects, etc could cause the price of the note to rise (for example), which would then lower the yield on the note. If the price goes to 101-00, the coupon rate stays the same, and so the yield to maturity drops. This is because the bond will mature at 100-00.

It is fair to ask why people would buy 10 year German Bunds at negative yields. They do because there is really no alternative. Banks won’t accept large deposits at even 0% interest because they have no way to invest those deposits. There is effectively no way for Siemens to just hold cash in a vault. So, they are stuck buying the Bunds. It really is a crazy situation.