You would do it the same way as any other function that you would write in C. So, if you have your function defined in a source file named myLibraryFunctions.m, anyone who wanted to use that function would include the header file where you define it (probably myLibraryFunctions.h, and then just make sure that they link with the object file (most of this will be done for you in Xcode if you simply create a file to house your "global" functions and include the header file for them in any source file that you access it from. Then just define it:
void analyzeThis(id anyObject);
void analyzeThis(id anyObject) {
    NSLog(@"Object %p: %zu, %@", anyObject, malloc_size(anyObject), anyObject);
}
But in reality, you would write whatever you wanted in your function. These functions don't have to be a part of any class definitions or anything like that. In this case, they're exactly the same as they would be in C.