Next spring unless they are a reblooming variety such as the Encore Azaleas. They bloom for about 1.5 to 3 weeks each spring. Cold weather will extend the bloom, while hot weather will shorten the time of bloom.

They are the encore variety. When can I expect their second bloom?
Sorry for such a basic question - this is my first time planting anything!

It varies. They need a lot of sun, at least 4 to 6 hours is best. Further north, the reblooming is not as reliable. August or September would be a good start. It takes a while because they bloom on the new shoots that open in the spring. They have to develop flower buds before they can bloom. Then they bloom lightly into fall.

The spring flowering display is the best.

Here is a link that might be useful: Encore Azaleas