There are several elements of a shower space that could be contributing to a leaking shower.
To fix this, turn the water off at the main water valve to your home and test the shower to ensure that the water has been cut off properly. Then remove the handle and look to see if the o-ring or washer has sustained damage. Replace these fittings if there is observable wear or damage alternatively if these fittings are in good condition, replace the faucet cartridge.Once you have completed this process. Put the handle casing and the main water valve back on and test to see if the leak has been fixed.
Whilst there, clean the shower head for any build up of mineral deposits which can impact water pressure and flow which can contribute to a leaking shower head. Soak the shower head in recently boiled vinegar and let it sit for 30 minutes. Remove and scrub with a small brush to clean the head of the deposits.It is worth wrapping a small amount of teflon tape around the thread before the reassembly of the shower head. Once the head is reattached, turn the main water valve and test the shower head to see if the leak has been fixed.
Fixing a shower screen leak is relatively easy. All you'll need a tube of silicone gap sealer and some rags and the rest is relatively straight forward. Firstly, make sure the shower space is clean and dry and then run a bead of silicone along the gap and gently scrape away any excess sealant. Use a rag to go over the area to smooth out any rough areas. Once you have sealed the joint, use sugar soap to clean up any remaining sealant.
As a general defence to widespread damage in these situations is a waterproofing membrane which protects the structure from further damage. This will not exclude all shower areas however as the building regulations prior to the turn of the century did not require a guarantee by a registered waterproofer.
Having a contractor who specialises in shower leak repairs and waterproofing will ensure that all the potential points of water leakage are corrected before the problem potentially escalates to a much more expensive and complex fix.
Hiring a professional experienced in this area may even result in avoiding the removal of tiles as part of the repair process which will save you time and money. However in some circumstances and depending on the damage caused by the shower leak, the best solution may ultimately be to remove the tiles, waterproof the shower and retile. The benefit of taking such action as soon as possible is that you will ensure that you mitigate the risks associated with prolonged water leaks.