A good way to establish the point of the leak is to place a piece of thick cardboard beneath the machine and give it a short run whilst empty.
The most common leaks are from the 'Sump Hose' which connects the pump to the tub and the 'Door Boot' / door seal. Items such as 'underwires' from clothing can poke holes through them.
To get to the sump hose it is a matter of tipping the machine backwards to allow access. Lean it against the kitchen work surface and wedge something beneath it if you are doing the job alone. It's best to have another person to stop the machine falling forward onto you and of course for moral support and comedy observation :) Sump hoses are normally held on with spring loaded circular clamps (hose clamps). You'll need an adjustable wrench / mole grips or very large pliers. These clips can be fiddly to remove but once you get the knack...etc. Be warned : you will need a lot of sacrificial towels on the floor first and DO NOT pull off that hose if it is directly above you :D
To access the door seal it requires removing the lid. Remove the rear bolts, slide the lid forward or backward and it will un-hook.
In some machines the door seal has a couple of large circular wire bands with tightening screws. Some have spring loaded ones. Others have compression bands and require a good deal of persuasion to remove (mind your fingers).
I would initially explore the door seal fully with my hands to save messing around. 9 out of 10 times the hole can be found without dis-assembling the machine yet. The next trick is then finding out whether or not you are comfortable removing and re-fitting it (as described above).
If neither of these are causing the leak then look for rusty trails inside the machine, follow them if possible to the source.
Before you do anything - check that the inlet hoses are screwed in tight - this is also another major cause of leaks and can be solved inexpensively.
you could always cut a small piece of urethane or silicone foam (closed cell only) and glue it into the gap on the static side of the opening. it would act as a live seal that could adapt to the gap or move as the door rotates.
you might want to take some time to really clean the existing sealant/caulk out from all over and redo it. also do the floor to shower pan joint. use a good solvent to clean everything up and bleach all surfaces prior to re-caulking. you have so much filth and mould there that new sealants wont stick. a properly sealed shower assembly wouldnt let water into your ceiling below even if the door seals are not working.
Best Answer
What you're looking for is a "replacement shower door gasket". I found what appears to be an exact match for what you need here:
Replacement gasket
Check the measurements against your own part to be sure.
Good luck!