There's a market for a product overseas but it's made in America. If I buy the product here but sell strictly overseas, how will I be taxed if at all?

If you are exporting to a EU address, you will have to pay all appropriate duty taxes and landing taxes there

Most countries charge tariffs on imported finished goods. In addition you will likely have business taxes in the country where you do business, and as a US citizen will also report your earnings to the IRS.

And although you didn't ask about it - you will need to obtain a license to sell the products from the company that manufactures them in the US.