I first wrote this back in 2005, and had a number of comments on a blog from people about how it had helped them, so I thought I'd dig it up and repost it here.
First of all, grab Knoppix, burn it to a CD, and spend a few days (or a few weeks, whatever you feel comfortable with) playing with it. Unless you go into the install option, the base CD doesn't install anything to the hard drive, so you can't harm anything. This is a completely safe, non-intimidating way for you to initially get your feet wet.
2. While you're exploring Knoppix, there are a few things to read which will really help you. This [tldp.org] will give you a very good introduction to Linux, in terms of a little history of the system, how to begin using it, and how some basic things work. Here [tldp.org] is another in-depth document about using Linux, leading on from the previous one.
3. Once you've gone through those two, (take as much time as you need) this [tldp.org], written by the same man as the introduction, will introduce you to the Bash shell, the textual command interpreter where with Linux, you'll likely be spending a lot of your time. This will ease you into scripting in what I think will be a very non-intimidating way. You will be able to try out all of these exercises with the Knoppix CD, and again, because the CD doesn't install anything to the hard drive, you needn't worry about destroying your existing system's contents while you learn. This [tldp.org] is another book on Bash scripting which to a degree follows on from that one, and will go into somewhat greater depth. Both of these should lead to you feeling very comfortable writing shell scripts and moving around to a degree on the system.
4. Here [tldp.org] is where we get to some meat. This document goes into compiling and installing generic Linux/UNIX software, and offers some basic applications and examples. Once you've gone through this, coupled with the material above, you should now have sufficient understanding to be able to compile and install at least a basic application yourself.
5. The [tldp.org] Pocket Linux Guide will take you step by step through the process of learning to make a small, bootable Linux system on two floppy disks. Although compiling a basic custom kernel is part of this process, the Guide contains a link to another document which explains very clearly how to do this, and given the background you will have received from the previous documents, this should not be difficult.
6. Once you have completed the Pocket Linux Guide, you will then be ready to proceed to this [linuxfromscratch.org] site, which is the homepage of the Linux From Scratch Project. Here you will be able to read an HTML-formatted book which will give you the necessary information to successfully build an entire base Linux system of your own, and a more pure boot CD than Knoppix to initially build it upon. The Linux From Scratch Project also has a sequel book, Beyond Linux From Scratch, which describes how to install, among other things, a full graphical user interface with the X Windows system.