Ways To Get Less Information
The first edition of the book is much more coach-focused than the second. Perhaps you have the wrong edition for your situation? (The rest of my answer assumes that you have the second edition.)
If you're looking for less information as you get started, you could try StrongLifts 5x5 instead, or look through the Starting Strength wiki and distill the important parts. The basics of the program are in the wiki. The basics of the techniques are on the wiki. That's probably your best bet.
The Inherent Problem
But whether we like it or not, there's simply a lot to learn. You'll need to read the book at least twice, and re-read specific sections as you find necessary. The only shortcut would be a coach, training partner or gym that is well-versed in the program. Even then, you'll be doing a lot of learning. That is the essence of barbell strength training.
In This Part I Try to Answer Your Specific Questions
For warm-up, I rotate all my joints from fingers to toes (with particular attention to all the articulations of the trunk), then do five minutes of moving around (running, skipping, air squats, knee raises) to get my heart rate up. Then I start squatting with the empty bar. I think that's pretty close to what Rip recommends, but I got the specifics from Tom Kurz.
I don't remember any particular cool-down for the program. I advise against sitting down immediately, lest you get tight.
Resting means not doing anything strenuous. His forums are a fine place to learn exactly what that means, but essentially: if you play other sports, run, do extra lifting, don't eat enough, (or eat way too much and you're already overweight), go on long bikerides or hikes, you are not resting properly.
The program is pretty simple. (It's only complex if you want to pick a variant, and there's a minimum level of complexity necessary for it to be informative.) Work out three times a week. Start with squats, then presses, then pulls. Squats are squats. Presses alternate between bench and overhead. Pulls alternate between power cleans and deadlifts. For each exercise, do five reps with the empty bar, then add fifty pounds (or so) and do four, and so on with more weight and fewer reps until you get to your working weight, where you do three sets of five for squats and presses, one set of five for deadlifts, and five sets of three for power cleans. Keep track of how much you lift in each exercise. Each exercise gets five (presses, cleans) or ten (squats, deadlifts) pounds heavier in each workout for as long as possible. When adding ten pounds isn't possible, add five. When adding five isn't possible, add 2.5 if available, or de-load the bar 20% in your next workout and resume adding weight.
If you need any more information than that, then you should be reading the book.