This is a basic into on making libraries for a unix/linux machine using standard gnu tools.

The things you need to know when compiling a static library are :

You compile each object file normally
Use ar to put the object file(s) into the library. This typically invoked as "ar rcv" with the objects.
The standard naming convention is libxxx.a, where xxx is the name of your library.

The things you need to know when using a static library are :

When you compile your code, use the -I flag to give header file location(s).
When you link your code, use the -L flag to give library location(s). And use the -lxxx flag to link your library, where xxx is the name of your library, this must be after the object files in the link command.

The things you need to know when compiling a shared library are :

You compile each object file with the -fpic flag. This tells the compiler to make it position independant. This is needed since the addresses will be physical not relative when the code is run.
Use gcc -shared to put the object file(s) into the library.
The standard naming convention is libxxx.so, where xxx is the name of your library.

The things you need to know when using a shared library are :

When you compile your code, use the -I flag to give header file location(s).
When you link your code, use the -L flag to give library location(s). And use the -lxxx flag to link your library, where xxx is the name of your library, this must be after the object files in the link command. In a Makefile LDLIBS and LOADLIBES are the standard symbols used for this.
When you run the program, you will need to have the library path known to the linker. This can be done by adding the path to /etc/ld.so.conf, setting LD_LIBRARY_PATH to contain your library path, or installing the library in /lib or /usr/lib ( or /usr/local/lib ).

If I can't install the library, I usually write a shell script to set LD_LIBRARY_PATH for me and run the program.

#!/bin/sh
export LD_LIBRARY_PATH=.
./$@