Foreword
If you just want to goof around with friends, a listen server (Create Server in-game) is probably good enough. Just remember to look at the last section for further customization.
SteamCMD
Start with installing SteamCMD. Use this page for guidance.
Install Source SDK Base 2013 Dedicated Server
NOTE: The one you download through Steam UI probably won't work. You should use SteamCMD.
Run SteamCMD and run the following commands:
force_install_dir my2013folder
login anonymous
app_update 244310
External dependencies (Linux)
Linux dedicated server files are missing some dependencies, which you need to get from TF2 dedicated server repository: bin/linux64/libsteam_api.so, srcds_linux64 and srcds_run_64. You can either download the entire thing through SteamCMD (app id 232250) or use other means to download just those three files.
The game also needs to see steamclient.so, which comes with SteamCMD:
# Might be somewhere else depending how you installed SteamCMD.
ln -s ~/.local/share/Steam/steamcmd/linux64 ~/.steam/sdk64
Install mod dedicated server files
Download the dedicated server files and place the zombie_master_reborn directory in my2013folder.
Run
cd my2013folder
./srcds_run_64 -game zombie_master_reborn +map zm_docksofthedead
What's next
Game server account
If you intend to make the server public, you need to attach a Steam account to the server. You can do so here. Set the app id to 243750.
Navigation meshes
Generally, most custom maps do not pack the required navigation meshes for zombie movement. You can find a community maintained repository here.
SourceMod
ZMR does not work with SourceMod out of the box. You need to install SourceMod gamedata for full functionality. You can get them here.