The main thing is not to panic and not to bounce around between speech therapists hoping that someone will magically get your child talking in two weeks. A speech delay at two years old is actually within the normal range, especially if the boy understands everything and is actively communicating with gestures. But you shouldn't just sit back and do nothing either.
Try first to create conditions at home that stimulate speech: comment on what your child is doing ("You built a tower, great job!"), read books together, sing simple songs, name objects. Often kids just don't get enough speech input - when there's a lot of talking going on around them, they start to catch up. While you're at it, observe how he hears things - does he react to his name from a distance, does he listen to music.
If after three or four months of active interaction there's almost no progress, then it makes sense to see a speech therapist - not for a course of sessions, but for a consultation and recommendations. The doctor ruled out serious neurological problems? Great. That means you're in a more positive scenario, you just need patience and consistency at home. You can also get his hearing checked by an audiologist at the same time, if you haven't already - sometimes that's the simple reason behind speech issues.