In the US, most normal intersections will either have traffic lights, a 2-way stop (that is, the drivers on one road must always stop, regardless of traffic), or a 4-way stop (where all drivers must stop, regardless of traffic). Some intersections will have something different, but that probably covers 95% of the cases.

The only one where there are issues is the 4-way. Those rules apply there, too. In fact, they apply any other case where the right of way isn't abundantly clear (like at a 3-way stop where the two drivers are both at stop signs).

(Those rules I quoted were specifically for the State of North Carolina, but I imagine that the rules are very similar, if not identical, in all other states.)