Depends on the platform. If you're using an eCommerce site, I usually plug in something like Avalara Tax which handles collection, real time rates, and remittance and stuff, but it's pretty expensive. If you're trying to do it on the cheap(er) and easy...find a payment provider who is the "merchant of record" (Example: Square). The merchant of record is required to pay the tax so you don't have to deal with it at all, but you'll usually pay some sort of revenue share for that.

Or you can just be a crazy person and setup business licenses everywhere.

I used Paddle.com and they do it for me.

At tookapic.com I use Paddle and they simplify taxes a lot for me. However along with that comes a lot of limitations. Their support reply time is also very slow. The API does not offer everything I'd want. For few weeks I used fastspring.com which does pretty much the same, but still - even more limitations in terms of design.

So for simple payment solutions there's Paddle.com and Fastspring.com. If you want something more advanced and flexible, I'm afraid you'd need to pay extra for services like Avalara.

quaderno.io – works with stripe/braintree and a few more. Takes care of VAT-MOSS and all the other countries headache