when you receive the check, go to www.your-site.com/admin/store/orders and click "view" on the order. on the top right you should see a link "receive check". click this link and follow the steps from there.

you should also note that the ubercart system takes into account that the check has to clear, so just because you've received the check doesn't mean you have been paid yet.

i don't know off the top of my head if the system sends a confirmation mail when you click "receive check", but you can always force it to at the bottom of this same screen. just change the status from "payment received" to "sent" and check the "Send e-mail notification on update" checkbox.