I just started my small business and wanted to buy a few supplies for it. I have several hundred dollars in Amazon gift cards that I received as personal gifts from people not associated with my business, and I wanted to be able to use them to buy business supplies for my business. How can I use them, for my business, and the amount that I spend off of them be able to be claimed on my business taxes?

Yes aslongas you spend off of?em for your biz related expenses, then you can claim the biz related expenses on yur Sch C of 1040.

I was told by some other business owners that you first had to “donate” the gift cards to your business, before you used them, and I had no idea how to do that. Any idea how to do that?

as yu can see,
your gift cards are the equivalent of cash therefore you need to list this as a cash donation. Note ;Contributions of $250 or More:
You can claim a deduction for a contribution of $250 or more only if you have an acknowledgment of your contribution from the qualified organization or certain payroll deduction records.

also once you made more than one contribution of $250 or more, you must have either a separate acknowledgment for each or one acknowledgment that lists each contribution and the date of each contribution and shows your total contributions.