I had to login just to help the one who needs help.
So, does your son know how to play Minecraft? I mean like Has he ever been familiar with the crafting and everything in survival? Well, it doesn't matter though, as long as he is having fun in that game. I will try to answer your questions in as simplest and in specific as possible. It will be based from my experience though, so I hope my reply helps you.
1. How difficult is it to update our version of Minecraft?
*Well since Minecraft has gone past 1.6.2 and currently at 1.7.4/1.7.2, you will need to download the new launcher from Minecraft.net, and yes the old launcher past 1.5.2 is not really working anymore. Just try to download the launcher, and I don't think no installer is included. The launcher is really easy to use unlike the last one.
2. Is there like a "Installing Mods for Dummies" link out there? I have tried several times to install Traincraft for him and each time it doesn't work it just makes him frustrated and very upset.
*I don't really know what traincraft is, but I will give you a link that looks promising to me. Try going to MinecraftDL at (Ad link removed), and they provide mods there with installation instructions. Note that every mods, not only from MinecraftDL but also to other sites, have their own installation guides, so keep an eye out for it. And I recommend that you should install Optifine, and other types that can make Minecraft more faster and enjoyable. That's where I get my mods in minecraft FOR ME though.
And don't worry. This site that you have putted on is the right place for Minecraft.
And hope my reply help you, and I hope that your son will enjoy more about Minecraft than me, because I only use my laptop, and I don't have any desktop with me, so it's really hard to play Minecraft here.
Anyway, I think that's it.