What methods, practices and conventions do you know of to modularize C code as a project grows in size?
Breaking the code up into libraries of related functions is one way of keeping things organized. To avoid name conflicts you can also use prefixes to allow you to reuse function names, though with good names I've never really found this to be much of a problem. For example, if you wanted to develop your own math routines but still use some from the standard math library, you could prefix yours with some string: xyz_sin(), xyz_cos().
Generally I prefer the one function (or set of closely related functions) per file and one header file per source file convention. Breaking files into directories, where each directory represents a separate library is also a good idea. You'd generally have a system of makefiles or build files that would allow you to build all or part of the entire system following the hierarchy representing the various libraries/programs.