You can take care when you write. Alternatively, you can mangle the language by failing to understand the differences between similar-sounding words. Many people alternate between the two.
Picture by David DeHetre
The essential distinction between 'alternate' and 'alternative' was neatly summed by a Lifehacker commenter last year:
Alternate = black white black white black white Alternative = black or white
The fact that many sloppy writers don't bother to distinguish between the two senses means that some people will argue quite passionately that 'alternate' can be used to mean 'alternative'. The Macquarie Dictionary (our authority on these matters) testily describes this definition as "disputed but increasingly common". I absolutely dispute it, and this misuse is often found in sentences that have other problems.
Take this example, sourced from a Google News search:
Google's suggested search terms are alternately helpful, funny and nonsensical — sometimes all three at once.
In this case, a better rewrite would be:
Google's suggested search terms are often helpful, funny or nonsensical — sometimes all three at once.
If you'd argue for a different rewording, tell us (and tell us why) in the comments.
Lifehacker's Mind Your Language column offers bossy advice on improving your writing.