use
LDFLAGS= -L<Directory where the library resides> -l<library name>
Like :
LDFLAGS = -L. -lmine
for ensuring static compilation you can also add
LDFLAGS = -static
Or you can just get rid of the whole library searching, and link with with it directly.
Say you have main.c, fun.c and a static library libmine.a.
Then you can just do in your final link line of the Makefile
$(CC) $(CFLAGS) main.o fun.o libmine.a