Are you saying that you'd connect grounds on each side of the isolator individually, but then not connect the two sides together?
Yes the ground between the arduino and the power of your circuit should not be joined. That is the whole point of an opto isolator to isolate the two circuits. If you do join the grounds then there is little point in having the opto.
it appears that they typically have a + and - connection for each side
Yes some do have other don't, if there is then keep them separate as they are not joined inside.
connect them to a GPIO pin and ground (respectively) on the control side, and then connect the switched side between 120V AC line and the device I'm controlling?
Yes that's how to do it, they should be isolated from each other.
it looks like it's really that simple...... or am I missing something?
No it is that simple, you are paying for it in the price of the SSR. You might be able to make one out of parts for slightly cheaper.