A corporations bonds will mature in 10 years. The bonds have a face value of $1,000 and an 8% coupon rate, paid semiannually. The price of the bonds is $1100. The bonds are callable in 5 years at a call price of $1050. What is their yield to maturity? What is their yield to call?

The yield to maturity is the discount rate which, when all the bond's remaining cash flows are discounted by such rate, their collective present value is equal to the bond's current price (in this case, $1,100).

As a general example, if there are n remaining cash flows C_1, \ C_2, \ ..., \ C_n , occurring at the end of periods 1, 2,. n, respectively, and the bond is currently priced at P, then the yield to maturity is that value r (expressed as a decimal) such that

P\ =\ \frac{C_1}{1+r}\ +\ \frac{C_2}{(1+r)^2}\ +\ ...\ +\ \frac{C_n}{(1+r)^n}

In other words, find a discount rate that makes the present value of all of the bond's remaining cash flows add up to exactly the amount of the current market price. That discount rate will then be the bond's YTM. You'll almost always have to use trial-and-error to find the correct YTM.

Finding the yield-to-call is the same thing, except you assume the bond will be called, and thus the "remaining cash flows" are only those which would occur under such assumption. I.e. it'll be the coupon payments up to the call date, plus the call price.

If you haven't already, the best thing to do is to become familiar with the process of determining the present value of a single cash flow or dollar amount. With that familiarity in hand, you'll then see that YTM work is nothing more than a simple extension of the basic idea to multiple cash flow scenarios. Best of luck with it!