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While it is simple to search by using help for most methods that have a clear help(module.method) arrangement, for example help(list.extend), I cannot work out how to look up the method .readline() in python's inbuilt help function.

Which module does .readline belong to? How would I search in help for .readline and related methods?

Furthermore is there any way I can use the interpreter to find out which module a method belongs to in future?

Don't try to find the module. Make an instance of the class you want, then call help on the method of that instance, and it will find the correct help info for you. Example:

>>> f = open('pathtosomefile')
>>> help(f.readline)
Help on built-in function readline:

readline(size=-1, /) method of _io.TextIOWrapper instance
 Read until newline or EOF.

 Returns an empty string if EOF is hit immediately.

In my case (Python 3.7.1), it's defined on the type _io.TextIOWrapper (exposed publicly as io.TextIOWrapper, but help doesn't know that), but memorizing that sort of thing isn't very helpful. Knowing how to figure it out by introspecting the specific thing you care about is much more broadly applicable. In this particular case, it's extra important not to try guessing, because the open function can return a few different classes, each with different methods, depending on the arguments provided, including io.BufferedReader, io.BufferedWriter, io.BufferedRandom, and io.FileIO, each with their own version of the readline method (though they all share a similar interface for consistency's sake).

From the text of help(open):

open() returns a file object whose type depends on the mode, and
through which the standard file operations such as reading and writing
are performed. When open() is used to open a file in a text mode ('w',
'r', 'wt', 'rt', etc.), it returns a TextIOWrapper. When used to open
a file in a binary mode, the returned class varies: in read binary
mode, it returns a BufferedReader; in write binary and append binary
modes, it returns a BufferedWriter, and in read/write mode, it returns
a BufferedRandom.

See also the section of python's io module documentation on the class hierarchy.

So you're looking at TextIOWrapper, BufferedReader, BufferedWriter, or BufferedRandom. These all have their own sets of class hierarchies, but suffice it to say that they share the IOBase superclass at some point - that's where the functions readline() and readlines() are declared. Of course, each subclass implements these functions differently for its particular mode - if you do

help(_io.TextIOWrapper.readline)

you should get the documentation you're looking for.

In particular, you're having trouble accessing the documentation for whichever version of readline you need, because you can't be bothered to figure out which class it is. You can actually call help on an object as well. If you're working with a particular file object, then you can spin up a terminal, instantiate it, and then just pass it to help() and it'll show you whatever interface is closest to the surface. Example:

x = open('some_file.txt', 'r')
help(x.readline)