I'm looking into selling a web application for US customers
Just do so.
I know this is a very complex topic so even a pointer would be helpful.
Ah - this is TRIVIAL. Seriously. I sell international all the time for years now. If you have a problem with that stuff get someone on board knowing the basics of running a business. Also you SHOULD have an accountant to talk to.
How are taxes worked out? Income tax, sales tax?
Sales tax for you would be European style VAT as per your registration / busienss country That is.... ZERO. NO VAT - VAT only applies to consumers (not companies, if they are VAT registrered) within the EU. You write out an invoices to the US company with their registration data and the tax rate is 0 (Non-Eu). Ask your accountant what to write exactly onto the invoice (depends by country).
Income tax: money you receive is your income. Whether this is EU or not, consumers or companies is irrelevant.
That is it. Simple like that.