Shaping Up with Weights for Dummies
Don't pay any attention to the title - this is a very smart tape to get if you're weight training for the first time. Instructor Tracy York talks you through a dozen exercises.
Weight Training for Dummies
This book covers the basics for anyone who wants to begin a weight-training program to improve their health. Women especially will find the approach of this book useful and not at all intimidating.
Kathy Smith: Timesaver - Lift Weights to Lose Weight
This tape proves why Kathy Smith is one of the top fitness icons. She offers two 20-minute, time-efficient weight-training sessions with enthusiasm and excellent instruction. She goes a little fast, so you will want to have either her book (listed below) as a supplement, or one of the others mentioned here.
Kathy Smith's Lift Weights to Lose Weight
With this book, Kathy gives you practically everything you need to start up a weight program, from lots of exercises to a training log. Add weights and you're ready to go!
Fitnessology - Exercise & Weight Training Techniques, the Basics
While the thought of having a real, Beverly Hills personal trainer in your own home may have its novelty, Raphael Picaud's instruction is anything but frivolous. This instructional video teaches you how to use both free weights and machines.
The Complete Idiot's Guide to Weight Training
Along with containing loads of information and being a great instruction manual, this book is also a very fun read!

It really makes no difference whether you want to go cheap or spend some serious bucks on dumbbells. For the most part, a weight is a weight and the rest is a matter of aesthetics (with a little bit of convenience thrown in, if you're considering adjustable dumbbells or Power Blocks). Basic iron dumbbells are fine. If they have a hexagonal shape so they don't roll around on the floor when you put them down, even better. Keep in mind that the covering on those vinyl or rubber-coated dumbbells are going to wear down eventually. You are going to need several pairs, because different muscles have different weight needs. Don't go too light, either. You want to fatigue the muscle. The average, beginning exerciser will generally want do about 10-12 repetitions of a move - after that, the muscle should be so tired that another rep can't be done with good form (advanced exercisers may want to do heavier weights and less reps, but right now, this is for those starting off). A big note for women: unless you're very, very weak, those one-pound weights are not going to work your muscles very much. You can start with three-pound dumbbells if you wish, but do realize you will grow out of them very quickly. Along with three (if that's where you must start), you should have pairs or five, eight, 10, 12 and 15 pound dumbbells. You will use them all. And no, these weights will not give you hulking muscles, or even close. Those guys with the giant arms and chests? They had to work very hard to get that way. Plus they're loaded with testosterone (which aids in getting muscles big) and you only have a little. So feel free to challenge yourself! If you do think your muscles are getting too big, lower the weight and increase the reps - you still want to "work 'til failure," you'll just do it in 15-18 reps instead of 10. Men - you'll be wanting heavier weights, of course. If you're new to this, start at 10 and buy them up to about 40. Don't go overboard on weight size if you're just starting out. If you lift heavier than your capabilities, you are really opening yourself up to injury. Stay in the 10-12 reps 'til failure range until you know what you're doing. Learn how to lift properly before you start showing off or going for real size, okay?

This is another item that doesn't have to be fancy. Just make sure it is padded, with a quality, leather-like material that won't wear out too fast. Ideally, you should buy a bench that can be adjusted from flat to incline to straight up, so you can do your weight workouts laying down or sitting up at a variety of angles. Decline, where your chest is lower than your hips, is good, but not an absolute necessity. If you're strapped for cash, you can always just buy a plain, flat bench - it's still a versatile tool.

You need a stable surface with a bit of padding to do floor exercises, so you really should have a mat. MatsMatsMats.com has a great selection. A mat should be long enough to accommodate you from the top of your head to below your knees when you lay down on it and thick enough so it doesn't hurt to kneel on it.