It's all pretty relaxed, with no registration required. Tenby will be busy and the road through town which leads to the harbour is closed to traffic during daytime in the holiday season. There's a couple of members of Tenby Sailing Club who post on this site, who may be able to advise if you can use their club's facilities.
Saundersfoot also gets busy, but could be an easier option for you. The main car park overlooks the harbour and you can launch off the beach there quite easily.
Milford Haven waterway is great for exploring by SIB - miles of deep water and pretty scenery, particularly the upper reaches. Lots of free slipways & parking.