First off, we're always talking C/C++ code here (eg: x86 ASM is a no-go).
For compiling existing libraries for use on the Wii, see the set of instructions I included in the
Freetype compile I did. This applies to other libraries as well. They call this "cross-compiling" - meaning compiling on one architecture (eg: x86) for another (PPC). Some libraries compile without any modifications required, while others may have "endian" issues, in which case the code needs to be modified to use big-endian. There may be other incompatibilities for various reasons (eg: C standards, buffer sizes, file access code, etc). But, again, many of the well-established and better written libraries already avoid these issues.
For using a library, you need to include it in your makefile (eg: -lmxml), and use an #include for the .h file.
For making your own Wii library, there are some best-practices (eg: global vars are bad), and other than that, just compile your code into a .a file, and you're ready to go! A library as far as the Wii is concerned is just some precompiled code, very little black arts voodoo magic is involved. ;)