Murray and I have been a therapy dog/handler team for 5 years. We love it. Besides visiting nursing homes/hospitals, we do educationall programs for children(our local library sponsors these yearly during 'Dog Week' at the library), have developed guidelines for a home visit brogram for Autisc children (we visit 3 Autistic brothers in our community), have participating in a school reading program, and recently visited our regional medical center (at their request) and gave a presentation on the roll of pet therapy in patient care to a group of future physicians. This is a short list, we've actually done a lot of other interesting things!
How to get started:
First, I would contact a couple of local hospitals and see if there are any members of pet therapy organizations doing visits there. This way, you can see if there is one particular organization which is active in your area, and can contact a local representative of that organization. If no one seems to be active in your area, contact a national group (like TDI) and they can put you in touch with someone locally.
Each organization is a little different in their requirements, but usually you'll have to attend an orientation meeting, have you're dog evaluted for temperment (I trained last summer to do dog evaluations for our local organization), and then complete some supervised visits. After that you'll be insured by the organization. (Note: some facilities allow non-certified dogs in to do visits, but in this age of litigation, I would not recommend doing this)
I'm lucky in that my local organization is extremely active in our community, and facilities overwhelm us with requests- there's never a problem finding something fun and interesting to do.
If you seem to be alone in your community after you get certified, just use your imagination- you can contact faciliites on your own to see if they want visits, you can contact local Cub Scout/Brownie troops to see if they want to learn about therapy dogs, etc.-
Hope that helps!