Assuming you are in Reykjavic and want to dive Silfra.
I used Magma diving. The guy I co-ordinated with was David, although I understand he is back in the UK, but Magma diving and his partners are still operating.
I stayed in a Bed and Breakfast (Butterfly hotel), a couple of streets back from the harbour. The shuttle bus service from the airport was very good. Going home, we booked the shuttle bus and the blue lagoon option, which was quite relaxing and suited our late afternoon flight and morning checkout.
We did take our own drysuits, thermal layers dry gloves and cameras.
One issue we had was the camera lenses fogging up because of the very cold water. (I learnt that getting a bucket of water when we arrived and dropping the cameras and lenses in it on arrival whilst we sorted kit reduced the problem of fogging.)
Gareth