To alternate is to take turns; an alternative is an option. When you wear your checkered blazer, the black and white squares alternate. But if you're not feeling like an '80s guitar hero, the green plaid jacket is a nice alternative.

Alternate can act a noun, verb, or an adjective, that nut. As a noun, it's a substitute, like the alternate who takes over for you in a game or in a jury:

Several, including alternates, have taken notes and kept lists of evidence. (Washington Post)

As a verb it refers to the act of something going back and forth:

So it went on all day — heavy showers that lasted for a few minutes alternating with brief, bright intervals. (Mrs. Herbert Strang)

As an adjective, it describes two options taken in turns:

The alternate jersey will have an interlocking SD on the left chest. (Washington Post)

Alternative can be an adjective or noun, too. As an adjective it describes something available as another choice, including alternative lifestyles. As a noun, it means one of two or more choices. Here are some alternative sentences:

We are coming up with an alternative plan, if Your Majesty will give us just a short time to do so. (The Assassination of Brangwain Spurge)

Diaspora, an alternative to Facebook, was founded by four New York University students in 2010. (Washington Post)

People often say alternate when they mean alternative, maybe because it's shorter. No one's going to freak out if you mix them up, but use alternate for what those checkerboard squares do on your rock star blazer, and save alternative to describe the music it makes you want to crank up.