There's a bunch of services that you can send your transactions to and they'll return sales tax data via API, your accounting software should have integration for them already. Worst case you can do them on a simple web form online (enter the address, types of goods, etc)
Those same services can also automate your tax filings with each state. It's not free, though.
Those same services can also automate your tax filings with each state. It's not free, though.