For windows, you can package the dll files in the same directory as your main program and they will be picked up automatically.
For linux, it would depend on your packaging. If you are releasing via rpm/deb/etc you can set a dependency on the packages providing the runtime library bits you require. Another option is to specify LD_LIBRARY_PATH in a sh script to point to your own lib directory, don't overwrite the value but append it as:
LD_LIBRARY_PATH=<my lib dir>:$LD_LIBRARY_PATH
I would not recommend polluting /usr/local/lib with any pre-compiled libraries you deliver unless they are part of your game!