Here are a few basic things to look into.
1. Correct Credentials; they should have completed a masters program and be nationally certified.
For speech therapy they should have MA, CCC-SLP or MS, CCC-SLP, next to their name.
2. Experience working in the area you are searching for.
3. Be on major referral lists: University Lists, Public School List, National Speech list (ASHA list) (American Speech Hearing Association)
4. Special organization list: e.g. I'm listed under the Stuttering Foundation of America List.
5. Be licensed with your State; occupational and professional license.
6. Have a city business license - if a private provider
The therapist should at least "enjoy" if not "love" their work and their clients. This makes a huge difference with building positive rapport for successful sessions.
I can truly say I LOVE WORKING WITH MY CLIENTS!