Learn Russian: Вчера мы ездили туда и обратно.

Because this is a completed round trip. In Russian, when you go somewhere and come back, you use the multidirectional verb. The phrase туда и обратно (there and back) makes it very clear that the trip is finished and involved multiple directions.

How do we know from this sentence that they didn't walk?

The verb ездили specifically means going by some form of transport (like a car, bus, or train). If they had walked there and back, the sentence would use the verb ходили.

I learned that там means "there". Why is it туда in this sentence?

Там describes a static location, answering "where is it?". Туда describes a direction of motion, answering "where to?". Since the verb ездили involves moving toward a destination, you must use the directional word туда.

Is туда и обратно a common phrase?

Yes, it is a very common set expression that translates perfectly to "there and back" or "round trip". For example, if you are buying a round-trip train ticket, you would ask for a ticket туда и обратно.

Why does ездили end in -ли?