The first thing you need is the right surfboard. Most people make the mistake of trying to learn how to surf on a board that is too short. They see pros riding short boards and think that's what they need. This is wrong and will only make you frustrated and give up trying to learn.
Make sure you get a surfboard that is a least 9' long. You want it to be thick and wide as this will insure it's buoyant and stable. A good choice for learning are those soft-top boards that are...are like giant Boogie Boards.
Practice these first steps on the sand before you get in the water:
1. Lay the board with it's fin, (or skeg), down in the sand so the top, (or deck), is facing up.
2. Lay on the board on your stomach so your head is about 2/3 of the way towards the front, (or nose), of the board. Since you will spend a lot of time laying on your board you should invest in a rash guard or other UV protective surf shirt such as a StayDry Shirt to protect your stomach from getting a rash and your back from getting sunburned.
3. This next part is done all in one, quick motion: bring your hands up near your chest and grab the sides of the board then jump up and bring your feet up to where your hands are so you are now crouched on your feet and holding the board. Be sure you bring your feet up and under you so you are on your feet near the center of the board and that one foot is ahead of the other, (which foot is up to you).
4. Slowly stand upright as you bring your arms out to the sides for balance. Be sure to keep your knees bent.
Practice this technique,(called a 'pop-up'), until you can quickly and smoothly jump to your feet in one motion.
Now you're ready to hit the water.
Go to a beach that either has small, gentle waves or lots of whitewater you can ride on. Whitewater, (or soup), is the water that rolls towards the shore after a wave has broken. It's the best place for learning as it will be easier to catch when you paddle. You can also have someone stand in the whitewater and push you into the wave while you lay on the board.
Enter the water pointing the nose towards the waves and lay on your board.
IMPORTANT: You want to lay on the board so that the nose of the board doesn't dip into the water OR point up out of the water too high. When you start to paddle you want the nose to be parallel with the water, just skimming the surface.
To paddle keep your head up, your legs together on the board and cup your hands as you reach out into the water and draw them back along the sides of the board. Bring them out of the water down by your hips smoothly and without a lot of splash.
Once you're out and white water is coming towards you turn and point your board towards the shore, lay in the correct spot, (nose skimming the water) and start paddling. When you feel the wave pick you up and start to push you without you having to paddle you're ready to 'pop-up', (see step #3).
It will take some practice but by the end of the day you'll have a lot of fun, get a great workout and be surfing. Just get yourself a rash guard and some board shorts and you'll be a total surfer, dude!