When you look on the internet for a music teacher, you should know a little about the organizations you might find there. In Delaware, the two most prominent music teacher organizations are Delaware State Music Teachers Association (DSMTA), which is affiliated with Music Teachers National Association (MTNA), and Delaware Music Educators Association (DMEA), affiliated with Music Educators National Conference (MENC). They are not really in competition, but each fills an important role in serving the citizens of the state. DMEA is primarily an organization of school music teachers, while DSMTA is mostly made up of private studio teachers. There may be a few teachers who are members of both groups, but generally there is no overlap.
If you want a private teacher, such as for piano lessons, DSMTA is probably where you want to look. Go to the MTNA website, mtna.org, and find the directory of nationally certified teachers, which will give you names and contact information of teachers who are nearest to your zip code. A teacher who is MTNA certified has passed rigorous examinations, and presented a demonstration of performances by his or her students that show a high level of competence as a teacher.
DMEA/MENC sponsors school-based activities, including Solo and Ensemble Festival, which is a performance evaluation in which students perform for adjudicators and receive feedback and scores/ratings on their performance.
Both organizations provide professional development activities for teachers, which help them to continue to grow as music teachers.
There are other websites you may encounter to help find teachers, but many of them are simply listing services, often for profit, that are designed to steer students to listed teachers for a fee. MTNA certified teachers are preferred, but there are many fine teachers who do not hold this certification, and certified members of DSMTA that you find through the MTNA website can help you to find those who are member of DSMTA/MTNA who do not yet hold certification.