Price

A common way of looking at a swap is to think of it as two bonds.
One with a fixed coupon and the other with a floating coupon.
The bond cash flows are then exchanged on the payment dates.

There are two common approaches for valuing a Swap
1) View each leg as a sequence of cash flows (similar to a bond) and then add up the present value of the future cash flows.
2) As a portfolio of forward rate agreements