Detect the operating system using two simple tricks:
- First the environment variable OS
- Then the unamecommand
ifeq ($(OS),Windows_NT)     # is Windows_NT on XP, 2000, 7, Vista, 10...
    detected_OS := Windows
else
    detected_OS := $(shell uname)  # same as "uname -s"
endif
Or a more safe way, if not on Windows and uname unavailable:
ifeq ($(OS),Windows_NT) 
    detected_OS := Windows
else
    detected_OS := $(shell sh -c 'uname 2>/dev/null || echo Unknown')
endif
Ken Jackson proposes an interesting alternative if you want to distinguish Cygwin/MinGW/MSYS/Windows. See his answer that looks like that:
ifeq '$(findstring ;,$(PATH))' ';'
    detected_OS := Windows
else
    detected_OS := $(shell uname 2>/dev/null || echo Unknown)
    detected_OS := $(patsubst CYGWIN%,Cygwin,$(detected_OS))
    detected_OS := $(patsubst MSYS%,MSYS,$(detected_OS))
    detected_OS := $(patsubst MINGW%,MSYS,$(detected_OS))
endif
Then you can select the relevant stuff depending on detected_OS:
ifeq ($(detected_OS),Windows)
    CFLAGS += -D WIN32
endif
ifeq ($(detected_OS),Darwin)        # Mac OS X
    CFLAGS += -D OSX
endif
ifeq ($(detected_OS),Linux)
    CFLAGS   +=   -D LINUX
endif
ifeq ($(detected_OS),GNU)           # Debian GNU Hurd
    CFLAGS   +=   -D GNU_HURD
endif
ifeq ($(detected_OS),GNU/kFreeBSD)  # Debian kFreeBSD
    CFLAGS   +=   -D GNU_kFreeBSD
endif
ifeq ($(detected_OS),FreeBSD)
    CFLAGS   +=   -D FreeBSD
endif
ifeq ($(detected_OS),NetBSD)
    CFLAGS   +=   -D NetBSD
endif
ifeq ($(detected_OS),DragonFly)
    CFLAGS   +=   -D DragonFly
endif
ifeq ($(detected_OS),Haiku)
    CFLAGS   +=   -D Haiku
endif
Notes:
- Command - unameis same as- uname -sbecause option- -s(- --kernel-name) is the default. See why- uname -sis better than- uname -o.
 
- The use of - OS(instead of- uname) simplifies the identification algorithm. You can still use solely- uname, but you have to deal with- if/elseblocks to check all MinGW, Cygwin, etc. variations.
 
- The environment variable - OSis always set to- "Windows_NT"on different Windows versions (see- %OS%environment variable on Wikipedia).
 
- An alternative of - OSis the environment variable- MSVC(it checks the presence of MS Visual Studio, see example using Visual C++).
 
Below I provide a complete example using make and gcc to build a shared library: *.so or *.dll depending on the platform. The example is as simplest as possible to be more understandable.
To install make and gcc on Windows see Cygwin or MinGW.
My example is based on five files
 ├── lib
 │   └── Makefile
 │   └── hello.h
 │   └── hello.c
 └── app
     └── Makefile
     └── main.c
Reminder: Makefile is indented using tabulation. Caution when copy-pasting below sample files.
The two Makefile files
1. lib/Makefile
ifeq ($(OS),Windows_NT)
    uname_S := Windows
else
    uname_S := $(shell uname -s)
endif
ifeq ($(uname_S), Windows)
    target = hello.dll
endif
ifeq ($(uname_S), Linux)
    target = libhello.so
endif
#ifeq ($(uname_S), .....) #See https://stackoverflow.com/a/27776822/938111
#    target = .....
#endif
%.o: %.c
    gcc  -c $<  -fPIC  -o $@
    # -c $<  => $< is first file after ':' => Compile hello.c
    # -fPIC  => Position-Independent Code (required for shared lib)
    # -o $@  => $@ is the target => Output file (-o) is hello.o
$(target): hello.o
    gcc  $^  -shared  -o $@
    # $^      => $^ expand to all prerequisites (after ':') => hello.o
    # -shared => Generate shared library
    # -o $@   => Output file (-o) is $@ (libhello.so or hello.dll)
2. app/Makefile
ifeq ($(OS),Windows_NT)
    uname_S := Windows
else
    uname_S := $(shell uname -s)
endif
ifeq ($(uname_S), Windows)
    target = app.exe
endif
ifeq ($(uname_S), Linux)
    target = app
endif
#ifeq ($(uname_S), .....) #See https://stackoverflow.com/a/27776822/938111
#    target = .....
#endif
%.o: %.c
    gcc  -c $< -I ../lib  -o $@
    # -c $<     => compile (-c) $< (first file after :) = main.c
    # -I ../lib => search headers (*.h) in directory ../lib
    # -o $@     => output file (-o) is $@ (target) = main.o
$(target): main.o
    gcc  $^  -L../lib  -lhello  -o $@
    # $^       => $^ (all files after the :) = main.o (here only one file)
    # -L../lib => look for libraries in directory ../lib
    # -lhello  => use shared library hello (libhello.so or hello.dll)
    # -o $@    => output file (-o) is $@ (target) = "app.exe" or "app"
To learn more, read Automatic Variables documentation as pointed out by cfi.
The source code
- lib/hello.h
#ifndef HELLO_H_
#define HELLO_H_
const char* hello();
#endif
- lib/hello.c
#include "hello.h"
const char* hello()
{
    return "hello";
}
- app/main.c
#include "hello.h" //hello()
#include <stdio.h> //puts()
int main()
{
    const char* str = hello();
    puts(str);
}
The build
Fix the copy-paste of Makefile (replace leading spaces by one tabulation).
> sed  's/^  */\t/'  -i  */Makefile
The make command is the same on both platforms. The given output is on Unix-like OSes:
> make -C lib
make: Entering directory '/tmp/lib'
gcc  -c hello.c  -fPIC  -o hello.o
# -c hello.c  => hello.c is first file after ':' => Compile hello.c
# -fPIC       => Position-Independent Code (required for shared lib)
# -o hello.o  => hello.o is the target => Output file (-o) is hello.o
gcc  hello.o  -shared  -o libhello.so
# hello.o        => hello.o is the first after ':' => Link hello.o
# -shared        => Generate shared library
# -o libhello.so => Output file (-o) is libhello.so (libhello.so or hello.dll)
make: Leaving directory '/tmp/lib'
> make -C app
make: Entering directory '/tmp/app'
gcc  -c main.c -I ../lib  -o main.o
# -c main.c => compile (-c) main.c (first file after :) = main.cpp
# -I ../lib => search headers (*.h) in directory ../lib
# -o main.o => output file (-o) is main.o (target) = main.o
gcc  main.o  -L../lib  -lhello  -o app
# main.o   => main.o (all files after the :) = main.o (here only one file)
# -L../lib => look for libraries in directory ../lib
# -lhello  => use shared library hello (libhello.so or hello.dll)
# -o app   => output file (-o) is app.exe (target) = "app.exe" or "app"
make: Leaving directory '/tmp/app'
The run
The application requires to know where is the shared library.
On Windows, a simple solution is to copy the library where the application is:
> cp -v lib/hello.dll app
`lib/hello.dll' -> `app/hello.dll'
On Unix-like OSes, you can use the LD_LIBRARY_PATH environment variable:
> export LD_LIBRARY_PATH=lib
Run the command on Windows:
> app/app.exe
hello
Run the command on Unix-like OSes:
> app/app
hello