Right so I did a quick google and this looks like an alright tutorial (https://www.zombiemodding.com/index.php?topic=1516.0) but I know there are others out there if you have a good look around the internet. There might also be one on ugx but I have no interest in linking from that site :P

As for everything else, I could spend a few weeks writing out exactly how to mod but I've not got the time :P So here is a load of some what helpful shit to get you started in the magical world of CoD modding for a hardly supported modding community.

Menu files are complicated little shits but easy once you figure them out and you can make some really cool shit once you've been able to do that.
http://think-clan.com/menudef/index.html#toc4.24 This site is a little dated but it explains and mostly shows off every little detail about what the menu files can do and how to use it. I do suggest using this as more of a reference so to actually learn menu files you'll want to take a look at the existing ones and try to understand them. Try doing small modifications and work our way up. You'll soon have figure them out.

GSC modding is relatively simple enough for anyone that knows a relatively high level language. Something like Python, Javascript, etc. The simple ones to work with. If you have no programming experience at all then once again I urge you to go and look at what the game already has. Try and understand it and then make small adjustments. I'd suggest looking at the zombie_powerup.gsc and see if you can figure out how to remove the bomb affect or increases the drop rate. Pretty simple shit for me because I've been doing GSC work for 9 years but should be a good starting level for you.

Heres some helpful resources for you to learn more GSC stuff from:
http://wiki.modsrepository.com/index.php?title=Call_of_Duty_5:_Modding just has everything you'll need to learn how to mod
http://wiki.modsrepository.com/index.php?title=Call_of_Duty_5:_Custom_Nazi_Zombie_Maps Has lots about mapping for zombies
http://wiki.modsrepository.com/index.php?title=Call_of_Duty_4:_mapping_sp and
http://wiki.modsrepository.com/index.php?title=Call_of_Duty_4:_mapping_mp have a fucking lot about how to map and how to do the finer things. Just because it's for CoD4 doesn't mean it wont work. They are basically identical games engine and mod tools wise. I've ported a zombie map to cod4 before and it took 5 minutes and some retexturing.

http://wiki.modsrepository.com/index.php?title=Call_of_Duty_4:_Scripting_Reference
http://www.zeroy.com/Script/
http://modme.co/scriptdocs/
are all great places to to get a full list of every function thats in CoD 4 and 5. Watch out though because each ones is just a little more incorrect than the last. One might show a function exists and there might not know it exists. Pretty annoying but what can you do :P

http://wiki.modsrepository.com/index.php?title=Call_of_Duty_5:_Scripting_Syntax_And_Grammar
http://wiki.modsrepository.com/index.php?title=Call_of_Duty_5:_Scripting_Basics
are both basically the same thing but can really help out when trying to understand whats going on in a GSC script. Each one explains it a little better than the other one.

http://wiki.modsrepository.com/index.php?title=Call_of_Duty_5:_Scripting_Common_Tasks
This shows you how you might go about doing some commonly needed things but a lot of the scripts are based around mp.

http://wiki.modsrepository.com/index.php?title=Call_of_Duty_4:_CoD_Script_Handbook
Last but not least this is a simple example of what the about 2 but written specially for cod4. it's an optional one :P

I hope all that helps. Sorry for giving you a book to have to go though but there is a lot to modding and even more to mapping so its a lot you need to learn to know what your doing and to eventually get good at it. I suggest not using other peoples shit as much as you can possibly help it. Upon people writing complete shit for this game they normally will not support it so you'll end up having to bug fix someone elses shit and it's just annoying beyond belief. Although the exception to that rule is guns and models. Thats another task in it's self :P To learn the fastest is to find someone that knows what they are doing and just be nice to them. They'll be happy to help most of the time and just don't spam them and let them reply in there own time. There probably wasting their time on BO3 modding ( ha ).