Nick, I think all the other answers are actually answering your question, which is how you link libraries, but the way you phrase your question suggests you have a misunderstanding of the difference between headers files and libraries. They are not the same. You need both, and they are not doing the same thing.
Building an executable has two main phases, compilation (which turns your source into an intermediate form, containing executable binary instructions, but is not a runnable program), and linking (which combines these intermediate files into a single running executable or library).
When you do gcc -c program.c, you are compiling, and you generate program.o. This step is where headers matter. You need to #include <stdlib.h> in program.c to (for example) use malloc and free. (Similarly you need #include <dlfcn.h> for dlopen and dlsym.) If you don't do that the compiler will complain that it doesn't know what those names are, and halt with an error. But if you do #include the header the compiler does not insert the code for the function you call into program.o. It merely inserts a reference to them. The reason is to avoid duplication of code: The code is only going to need to be accessed once by every part of your program, so if you needed further files (module1.c, module2.c and so on), even if they all used malloc you would merely end up with many references to a single copy of malloc. That single copy is present in the standard library in either it's shared or static form (libc.so or libc.a) but these are not referenced in your source, and the compiler is not aware of them.
The linker is. In the linking phase you do gcc -o program program.o. The linker will then search all libraries you pass it on the command line and find the single definition of all functions you've called which are not defined in your own code. That is what the -l does (as the others have explained): tell the linker the list of libraries you need to use. Their names often have little to do with the headers you used in the previous step. For example to get use of dlsym you need libdl.so or libdl.a, so your command-line would be gcc -o program program.o -ldl. To use malloc or most of the functions in the std*.h headers you need libc, but because that library is used by every C program it is automatically linked (as if you had done -lc).
Sorry if I'm going into a lot of detail but if you don't know the difference you will want to. It's very hard to make sense of how C compilation works if you don't.
One last thing: dlopen and dlsym are not the normal method of linking. They are used for special cases where you want to dynamically determine what behavior you want based on information that is, for whatever reason, only available at runtime. If you know what functions you want to call at compile time (true in 99% of the cases) you do not need to use the dl* functions.