The taxis on La Palma have their own website in English and Spanish (with German coming shortly). It lists all their various services. Obviously you can call a normal taxi for a single trip, but they also have 8-seater taxis for bigger groups, and at least one taxi which can take a wheelchair.
They have a series of standard tours, which are great if you want to see more than a sliver of the island and you’re just here for a day from a cruise ship, or nervous about driving on the “wrong” side of the road. They can also drop off walkers or cyclists, and pick them up later.
The man who handles the bookings is more comfortable with written English in an email, but he says he usually manages on the phone anyway. So if you’re phoning, I’d recommend allowing a little extra time, particularly if you have a storing regional accent.
The website is La Palma Taxi