You can think of it the same as any other investment (specifically a bond) it's no different.
While you own it, the periodic payments during the year are interest payments. At maturity, you may have a long term capital gain or loss depending how much you paid. Most folks are buying new/original issue CDs. You pay $1000 face value and you get back that $1000 at maturity - no gain or loss.
Now, CDs may also be purchased or sold in the secondary market. In this case, there may be capital gains or losses when sold or at maturity since you may get back more or less than the original purchase price.