The best place to ask questions about dive operators is a diving specific forum. The Dive Forum .com would be a good start.
I would strongly advise you to research and contact an operator before hand as some can be extremely sketchy.
Without knowing your experience I would recommend two shops on the Island. If you're in Playa Blanca then Rubicon Diving are very hard to beat. A very well run operation that cater for all levels of diving. This is also the best (only) choice for technical diving on the island. However, I'm guessing if that's what you're after you'd know.
If you're in Costa Teguise or Puerto Del Carmen then I would recommend Calipso (based in Costa Teguise). No brainer if you're staying in Costa Teguise. English operators and a good set up. They have mini buses that travel up and down the island and they go to the best variety of sites. Some of the best diving is up north near Mala (lava caves). They'll pick you up from either resort.
I would not recommend a Puerto del Carmen based operator. They have great diving just off the beach. It's super easy. However, this makes them lazy. They're unlikely to take you anywhere else. Rubicon and Calipso both dive the Puerto del Carmen sites but you also get the variety of diving at either end of the island.Edited: 05 June 2018, 16:35
My husband always uses Carlos and team at non stop diving up the steps by the burger king, on the left upstairs. Very central and excellent standards