At the risk of appearing to lay a guilt trip on his readers (all two of them), Mr. Rewrite will note that he worked through illness to produce this week's video blog on first come, first served. That explains his froggy voice.
Here's the text takeaway: It's first come, first served (not first serve). If you use a noun such as "basis" after it, it's a phrasal adjective and takes hyphens (first-come, first-served basis). It's best to put a comma between first come and first served. All of this is courtesy of Bryan A. Garner (cue angelic chorus).
The media don't do very well with this. Better than a quarter of uses on Google News are the erroneous first come, first serve/first-come, first-serve.
Why "served?" You're basically saying that the first to come are the first to be served. There's a fancy grammatical explanation, but Mr. Rewrite is groggy from cold medicine and is heading for bed.