Sales taxes are charged at the state level. It will depend on the physical location of the web store. If the state it's in charges a sales tax, and residents of that state must pay that sales tax when ordering.
For out-of-state orders, in most cases, you won't be charging sales tax. Some states, such as New York, have laws on the books that ALL out-of-state purchases, be they online or at a store, are charged NY sales tax. But in most cases, the law is nearly impossible to enforce and it's left to the purchaser to report the sale on their taxes (or not). But NY is making arrangements with major web retailers such as Amazon to charge the state tax for them rather than relying on the kindness of NY taxpayers. I'm sure they use some sort of "carrot versus stick" approach, threatening legal difficulties if the retailers don't comply.
The US doesn't have anything like VAT in Europe. Sales taxes are paid by the buyer. There's probably business licensing fees and business taxes, but they're tied to overall income rather than a specific product or sale.