This tutorial covers how to export files from an MPQ.
The first thing you will need is an MPQ editor, for example, Ladik's MPQ Editor. Download it, install it, and open it up.
Open the MPQ you wish to extract or add files to. In this case, I'll be choosing the main StarCraft II MPQ, which can be located at C:/Program Files/StarCraft II/Mods/Liberty.SC2Mod/base.SC2Assets (Assuming you have the same StarCraft II install as I do).
Navigate to and select the files you wish to extract.
Right-click them and select Extract, and choose where you want them to be extracted to. They will be extracted in a folder system that mirrors how they were stored in the MPQ. In this case, they'd be stored in C:/.../Assets/Textures