The following articles give general information on how learning disabilities are identified. Some of them list national organizations that may give you specific information about testing facilities. Be aware that if diagnosis is needed for the purpose of qualifying for special services or accommodations under federal law, it is important that a specialist licensed to diagnose LD and/or ADHD completes the assessment.
To find a testing facility, ask a physician for a referral or contact the special education office of your local school system. If you live near a college or university, you can inquire about whether they have an office that provides support for students with disabilities. They may be able to administer tests there, or recommend a location that can.