There are different aspects to modding. I started to create custom content with Jeremy McGrath's Supercross 2000 for the PS1, making custom tracks. I loved it so much, I'd spend hours making new combinations.
Things get pretty foggy, but I'm pretty sure my first game I actually modded was Halo: Custom Edition with the SDK, the Halo Editing Kit. It came with a proper set of tutorials, and on the web there was plenty of documentation as well. This was not enough, though, and I went out of my way to buy games that either had SDKs or community-developed tools to mod games, including (but not limited to) Freespace 2, F.E.A.R., Source-based Games, LegoRR and Flight Simulator X. The more I modded, the more I learnt about computers in general, and the more I was inspired to try other programs and learn to program, model, animate, create sounds, movies and level design. Eventually I downloaded special programs like Adventure Game Studio, Unity, UDK, CryEngine, Game Maker and so much more. They're very good engines with great support and help documents, designed to allow anybody to make a game.
The key is to find tutorials on the web, written in a style suited to you, and following them to the letter at first, and then mixing them up and trying out new things, until you become confident with the process and you can do it your own way. Sometimes authors will take odd steps or a long path for different reasons, so I like to pursue finding out why the author performed all the steps they did, and what they actually do towards the finished product. Of course, one way is to self-teach, as I (mostly) did for animating (help from Cirevam and some web tutorial to enhance my knowledge and help me do somethings I would have never thought of, of course). Play around with a program for an hour and you might learn some interesting new things. Of course, it can never beat help from a professional, but it's a good way to become acquainted with the basics.
One other thing, you can learn to program at Code Academy (google search them). They're brilliant online, free, tutorials that teach you exactly what you need to know and give you practical experience, and tell you every mistake you make so you can improve yourself. Also, I learnt C through the C All-In-One Desk Reference for Dummies, with author Dan Gorkin, whose amazing at writing his self-help books. Once you do learn, it's about first considering the problem, and looking at all the steps you would need to perform to create the solution. Break it down to some very simple steps, and you'll be able to code a program in no time.