I am thinking of purchasing a new wheelset for my road bike. Do wheels ordered online usually arrive ready to ride, or do they require some construction?
Depends on where/how you purchase them and the quality of the wheel, but generally pre-built wheels need a check-over for appropriate spoke tension/truing out of the box. You can either check this yourself or pay a bike shop to do this for you.
You can avoid these checks at your own risk, obviously. But, I wouldn't recommend it, especially if they aren't high quality wheels to begin with.