I claimed my son as a dependent on my 2020 taxes and shouldn't have. When and how can I amend this?

  You cannot amend a tax return that was just accepted.   You have to wait for it to be processed by the IRS.  Trying to send in an amended return while they are still processing the original return could confuse things and delay your refund for months.

Do not try to change anything on your return now.  When you amend, your Form 1040X has to be prepared from the return exactly the way it looked when you filed it originally.   You have to wait.   Once your return has been processed you will complete a Form 1040X   --- which is not yet available --- and submit it to amend the mistakes made when you filed your original return. It takes the IRS at least four months to process an amended return.

The 2020 Form 1040X does not become available until the end of February 2020 (subject to change).

If your son  -- or the person who can claim him -- files after you then their tax return is going to be rejected when they try to e-file.    He cannot e-file this year at all even if you amend.   He will have to print, sign and mail his return.