If there is a street with two lanes that merge into one, who has the right of way when they both go straight? Is it the person on the right or the person on the left? And how would the person who doesn't have the right of way know when to go?

The traffic in the merging lane gives way, merges, into the continuing lane, Like an on ramp of the highway.

If there are not any signage or road markings indicating which lane needs to merge the left lane would have the right of way.

There should be a sign posted before the merge. Example, in the right lane there should be a sign that says right lane ends, merge left.

And there should be a sign in the left lane that warns of merging traffic.

UK answer: If there are no signs/road markings to indicate otherwise, no one has priority and you merge in turn.