When and where do I pay taxes on a gift card I won from a raffle?

Basically, I have won a gift card for $3000 from a Charity Raffle for Best Buy. This was through my company so I am not sure if I have to claim it or if I just pay the sales tax.

If it shows up on your W-2, it's part of your wages. (You mentioned this was through work.)

If it shows up on a 1099-Misc (or not at all), you list it on line 21 as a prize on your 1040.

Sales tax has nothing to do with this.

This would be considered prize winnings, I believe. Ideally, the charity would send you a 1099 form to file with your taxes. I'm not an accountant, but I think if the charity does not report that you won this, the IRS would never know and you wouldn't have to declare it. I mean, legally, you probably should, but they would have no way to know.
I had to pay income taxes on my winnings when I won on Jeopardy two years ago, but they sent me a 1099 at the end of the year to file with my taxes, and I had to pay estimated taxed in the calendar year that I won--but that was a lot more money than this is.