Start with small simple projects with straight lines, then move up to more complicated projects. Pillows cushions are a good start; everyone likes to take naps, and it's all straight lines sewing. From there pyjama pants or a t-shirt is next, it adds curves to the mix and it's easy to fit.
But before that, learn all there is to know about your sewing machine, learn how to thread the bobbin, how to thread the needle, how to wind bobbins. Learn how to change feet, learn which feet are used for what. Learn how to change the needle, how to read the numbers on needles and why you never sew jeans with a 75 needle and why that 110 will wreck your chiffon.
practise sewing on scrap cloth and don't make anything. just make straight lines. Make circles, draw curved lines on fabric and practise following curves. Try to sew a corner.
Become familiar with the iron. Pressing is as important as the sewing machine. Learn how to press seam, learn how to turn and press corners, learn how to turn and press curves.
Once you are familiar with much of this boring practice and learning stuff the rest is easy. A seam is a straight line with a curve somewhere. A collar is straight lines and a corner. A zipper and neck facing is a circle and a straight line. Welt pockets are just a series of straight lines.
Reader's Digest complete book of sewing covers everything you'll need to know. It's a great one stop reference. And something you need to keep close by. it will enhance the pattern instructions and clarify anything you might neeed help with. Simplicity and Kwik Sew have patterns designed for beginners and all patterns come with detailed instruction sheets. Follow the instructions! Read them through before sewing, don't skip steps, don't jump out of order. They are designed to help you make the most out of your fabric and pattern.
Don't try to sew without a pattern, it will only end in frustration and wasted time and fabric. Trust me, I teach and my most popular class is "beginners in crisis: I thought I could do it without a pattern!" Kwik Sew has a line called Kwik Start, each pattern is like having me looking over your shoulder, but far less creepy and without my dangly necklaces jingling in your ear.
It takes time to learn, there is a learning curve and your first attempts might not work out too well. Try to keep track of what went wrong and make notes so you don't repeat the mistakes. I keep a record of everything I make, fabric samples, sketches what went wrong, what went right, and how to better accomplish the same item next time. These notes have become a valuable reference for me and i use them often. and Like most skills it does take time and effort to learn. no one is born a natural sewer, everyone has to learn the skill.
The essential tools are A good sewing machine, A pair of scissors that will be used for fabric only. Don't skimp on scissors, you can sew with a cheap sewing machine but cheap scissors will only make things difficult. A good iron that had variable steam and variable temperatures. Don't bother with "professional" systems made for quilters or tailors, a good household iron will work fine. Rulers and measuring tools including a basic 12 inch home/office/school ruler, an 18 inch metal ruler, a 6 inch multi purpose sewing gauge, and an extra long tape measure. Pins and hand sewing needles. Look for long dressmaker's pins, they will handle anything and everything and are easier to use than standard or short pins. They are often sold as "dorcas" pins. Pin length and gauges used to have odd names, dorcas referred to long dressmaker's pins. You don't need a whole bunch of different pins for different fabrics; all i ever use are that one type. Other notions are optional, you can buy them as you have a need for them.
Here are a few links that might be helpful
about.com has an extensive site filled with help for beginners: http://sewing.about.com/
Kwik Sew's learn to sew start page: http://www.kwiksew.com/learntosew.cfm
The simplicity pattern company's sewing classroom start page: http://www.simplicity.com/t-classroom.aspx
Watch out for some wikihow diywiki and ehow diyhow and video howto sites, the information is from users, many who have no qualifications and little business telling other how to sew. They can be confusing, miss steps and in many cases they are wrong. And videos aren't always easier to follow than books. A good book can sit by your machine, and you can check it often.
And that's the basics. learning to sew is about practise making perfect and the willingness to learn as you work.