The straight answer
No advance visa. A US passport holder flying to Dubai receives a free visit visa on arrival, valid for 30 days, stamped at immigration. It is the rule the UAE Embassy publishes for US citizens, and it is the answer this site's directory records for the US to UAE route. There is no application, no fee and no approval wait; the preparation that matters happens before the flight, not at a consulate.
The conditions that actually bite
Three of them. Your passport needs at least six months of validity from arrival; airlines check this at the desk and refuse boarding on less. The 30 days run from entry, and overstaying draws daily fines, so a long trip needs a plan, not optimism: the visa can be extended through official channels for a fee if you arrange it before the days run out. And the on-arrival visa is a visit visa; it is not permission to work, which is the mistake that turns a holiday into a legal problem.
Why some guides say 90 days
Because for other passports it is true. Several nationalities receive 90-day stays in the UAE, and guide pages that copy each other's tables sometimes print the longest number against every flag. It is a useful warning about this whole category of page: the day limit is passport-specific, which is why this site's directory is organized as a passport matrix rather than a list of countries. For a US passport, the number is 30.
Check the route, not just the destination
If your Dubai flight connects, the connection has its own rules; run it through the Transit Visa Checker. Destination sorted, layover sorted: the trip is ready.