Do changes in the price of a bond cause the yield to move? Or is it the change of rates and consideration of other risks that cause the yield to change which then affects the price of the bond?
One other thought to add to the answers:
Yield is an effective way to compare bonds that have different coupons and/or maturities. So two bonds that pay different coupons may have very different prices, but may have the same yield.
So in a mathematical sense, yield is a function of price (among other things). But in the practical sense, price is based on the yield that a buyer expects to earn from the bond, based on the yield of other bond of equivalent risk.
In theory, bonds sold on the open market can be bought at any price that buyer and seller agree.
In practice, pricing is relative to many factors. Typically, the market seeks the same yield from bonds that are considered to carry the same risk. This makes secondary-market price a function of yield. When risk is hard to peg rationally (e.g. during the Global Financial Crisis), price becomes dominant (sellers want to recover 'anything' they can). In that context, yield becomes a function of price.
A bond's price changes because buyers and sellers react to change in rates and to company news if it's a corporate bond.
Yield is simply a function of the bond's annual interest, its cost and the number of years until maturity.