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Sure, it's pretty simple (unless you mean an UTAU, a program that lets you make your voice into an actual UTAU, then I can't quite help you).
If you mean the fan-made kind, though, it's pretty easy.
First, you have to choose where the voice comes from (who will it be based off?).
You can use your own voice, and sing it yourself, then edit and add effects to it to make it different (like the Vipperloids, they had human voices edited to sound Vocaloid-ish to trick people).

OR you can base it off an already existing vocaloid or UTAU, like how Akita Neru is based off Miku. You can pitch up, pitch down, or change the effects on the song to make it different. If you do this, remember to credit the person who made the song you edited, or link the original. Be sure to also remember those voice setting for other songs.

The next bit is all designing. Draw (or have someone else draw) what you want your character to look like, create a personality, maybe a character item, and done, a fan-made. Give them a gender-bend if you're feeling creative.

EDIT: Lol, I almost forgot, to edit, you need a music editing program, or even a video making program, as long as it lets you pitch or change effects. Audacity is free and is for PCs, and Garageband is great (and free) for Macs, from my experience. Windows movie maker is for windows and iMovie is for Macs.