I accidentally double paid my income tax due amount this year. We didn't realize it charged our credit card and sent a check as well. How can we get that refunded?

I assume you're talking about federal income tax. First wait a few weeks. There's a good chance that the IRS will notice the overpayment and send you a refund without your having to do anything. If not, you'll have to call the IRS at 800-829-1040 to straighten it out.