|I assume you have some way of extracting zip files.
To install 'Total Conversions', extract the contents of the zip file in your Liero folder, overwriting the original files.
To install maps, extract the zip file of the map you downloaded. Move the file with the .LEV extension to your Liero folder. That's all. In Liero you can go to "Match Setup" and then "LEVEL" to select the level you installed.
To install skins, rename the file LIERO.CHR to something else, like ORIGINAL.CHR. Extract the zip you downloaded and move the CHR file to the Liero folder. Rename that file to LIERO.CHR.
To install new sounds, rename the file LIERO.SND to something else, like ORIGINAL.SND. Extract the zip you downloaded and move the SND file to the Liero folder. Rename that file to LIERO.SND.
To install new weapons, palettes or fonts you need additional software. Unfortunately that software is not available for OSX. If you know how to run DOSBox or Wine, you could try using that and run LieroKit, LieroM8, Liero CDC (all for Windows/Wine) or Liero Stuff Activator (for DOS/DOSBox).