So if I buy something, then sell it later, that first purchase should be considered a "resale" purchase, right?
In fact, if you can't provide a reseller's certificate (or license, the exact term depends on the state) then the seller generally must collect a sales tax on the sale.
However, you can only deduct items so acquired for business purposes, not for personal purposes.
I think this means that paying $10 would reduce your income tax by $3 (if income tax is 30%). This is different from getting a 100% credit ($10) which is what you'd get with a VAT system.
If for some reason you can't offset your input VAT, then you get the same deduction against your income as you would for a sales tax, because it's part of your expenses. BUT NOTE: that if the acquired good is depreciated, then in both cases (VAT or sales tax) the tax-related deduction is spread over several years rather than all at once.
Typically you don't pay in the first place, rather than getting reimbursed (EDIT: AFAIK). It also depends on the state, so I can't give a general answer. To give a concrete example, however, I'll use Washington state:
https://dor.wa.gov/taxes-rates/retail-sales-tax/reseller-per...
And here's a deeper link specifically for the actual action of applying for a reseller's permit, as linked in the sidebar of the above page:
https://dor.wa.gov/taxes-rates/retail-sales-tax/reseller-per...
EDIT: Okay, looks like there are deductions / reimbursement options as well, TIL:
https://dor.wa.gov/taxes-rates/retail-sales-tax/reseller-per...
Also, some retailers let you file your resellers license with them and then they don't charge you sales tax because they know you are a vendor who is going to resell it. This system is often abused by small businesses who buy personal items along with their business items and then don't pay tax on their personal items. In theory they have to file use tax at the end of the year (the same use tax you're supposed to file if you buy something out of state and aren't taxed on it), but most people don't.