This is for 1.1.0.4.
Download either Visual C++ Express or MinGW.
Get this file
Extract it with your favourite program and put the "source" directory in your main AssaultCube folder in Program Files.
MinGW:
1. From the start menu open the "MinGW Shell"
2. Navigate to AC's source folder ("AssaultCube_v1.1.0.4\source\src") using cd to change the directory. You must use forward slashes "/" instead of the usual backslash "\" for showing sub-directories, and use backslashes to specify spaces
i.e. C:/Program\ Files/AssaultCube_v1.1.0.4/source/src
3. Type "make" (no quotes, of course)
4. Be patient
It's quite possible that this will compile fine but when you try to run it, it will complain that it's missing some libraries (such as libstdc++.dll, libgcc.dll or something similar). The best solution for this seems to be to link statically to these libraries.
EDIT: If this is the case, open "Makefile" (in /src) in your favourite text editor that isn't notepad (Notepad won't split it up into individual lines).
Go down to where it says CLIENT_LIBS= -mwindows ...
At the end of that line, after "-lwinmm", type "-static" and save the file. This will make the executable file a bit bigger, but if you're only compiling it for yourself, this shouldn't be much of an issue.
As for compiling with Visual C++, I can't help you. I've never used it, although I hear it's quite simple and it's what tempest recommends.