Using the web browser, how do you use a lockable door. 5 read-throughs of http://docs.textadventures.co.uk/quest/tutorial/using_lockable_exits.html isn't helping in the slightest.

I don't see how it can be explained any better than it is in the tutorial you've linked to.

Any explanations you get are simply going to be repeating what's said in the tutorial.

Just take your time, read it carefully and follow the steps.

Very basically, let's say you have a room with an exit and a key on the floor.

You 'lock' the exit (as explained in the tutorial), then 'unlock' it (as explained in the tutorial) when they players types 'take key'.

It is not hard, but demands some steps in order to make it work.

1- Create room1
2- Create room2
3- Create an Object named Door at room1
4- Create an Object named Key at room1
5- Create an exit from room1 to room2 and make sure the exit be locked.
6- Give a name to the Exit, so Quest may identify it.
7- Add the Use/Give feature to the Key.
8- Set a script to Key for When used on another Object. The object will be Door. This script is of Object type, the one labeled "Open Exit". Then set the parameters with the name of the Exit you created on step 5 and named at step 6.

Try this tutorial:
https://github.com/ThePix/quest/wiki/Keys-and-Locks