You can now access the visitors centre from the new Woolwich Arsenal DLR station. It has an information desk on your left near the top of the escalator. They will direct you to the nearby bus station. Ask the bus driver to let you know when to disembark, (the Barrier is some way beyond the path that leads to the Centre).
Staff at the Centre are very friendly and helpful. Light snacks, tea, coffee and soft drinks at the Cafeteria are reasonably priced.
Downstairs there are fascinating displays of pictures, maps, articles etc on the history of the Thames and the various schemes proposed to prevent inner London flooding. Be sure to watch the short documentary film about the building of the Thames Barrier.