Sometimes the Thursday or Friday paper will have a list of weekend events. If you listen to a classical or public radio station, you're familiar with their announcements of upcoming events. Sometimes a station will play recordings of music that will be heard in concert. Call your local station and ask them when you can hear information about live concerts. Many concert-giving organizations publish a brochure listing all their concerts for the season.
Some organizations have summer seasons, or produce special festivals that run for a shorter time.
You can call these organizations and request a brochure. Musicians learn to perform by performing, so there are always concerts by young musicians. These events may not be widely publicized, but usually the public is welcome. Look for concerts at college and university music departments, at high schools, at music schools, and at music stores. Your area may have a youth orchestra or youth choir.