Procedure for updating a specific mod:
1) Open the DayZ Launcher.
2) Click MODS on the left panel.
3) Locate the mod you wish to update. You can use the search box on the top right.
4) Right click the mod and select REPAIR.

If the mod is already updated, nothing will happen. If it needs to be updated, it will be updated.

5) Click SERVERS on the left panel.
hopefully you will see the server either in the FAVORITES tab or the RECENT tab.

6) Move the mouse over the server, you will see a big red JOIN button. Click it.
7) Click the SETUP DLCS AND MODS AND JOIN button.

This will load all required mods and join the server.