Whether getting a lift to the corner shop, covering the four corners of the world or simply as a bit of general knowledge, there is a method to the madness of hitchhiking. Although it can seem daunting and complicated, it really isn't. Hitchhiking is a great way to meet people while getting you somewhere.

[edit] Steps

Pick a destination. Decide where you want to go. It’s a good idea to make a poster indicating in big, clear letters the place or direction in which you're heading.
Start in a good location. Hitching in cities is not highly recommended. It would be worth your while to spend a small amount of money on a bus to get you just outside of the city. Find a spot where the traffic isn't moving too fast. Not at, but near an intersection, or perhaps within a low-speed zone, and make sure there is ample space for a car to pull over, not just next to you, but at least 6 car lengths up the road.
Flag a ride. Stand on the side of the road facing oncoming traffic, not intercepting, but clearly visible to oncoming vehicles. It is important to find a spot along the road where it is safe for them to slow down and pull over. Extend your arm outwards, pointing towards the road, parallel with the ground, while holding your hand in a ‘thumbs-up’ position.
Smile! Show drivers that you are happy and cheerful.
Wait. Be Patient.
Talk to the driver of any car that stops, open the door, and confirm that they are going in the desired direction, or at least a desirable destination. Speaking with the driver is critical, because you can assess your comfort level with the driver. If you question your safety, don't be afraid to say no--another ride will be along shortly. Otherwise, find a spot for you and your stuff, get in, enjoy the ride and get out when requested.
Repeat above steps until destination is reached.

[edit] Tips

Don’t hitch in places where it is important for the driver to concentrate on the road, especially at crosswalks or areas where children are at play.
Comfortable clothes and shoes are important. Sometimes you will cover more road on foot than in an actual car just in an attempt to find the right spot.
Many drivers will be more likely to pick up a hitcher who appears to be walking. In reality, it probably won't get you to your destination any sooner, but it can help psychologically, in that you're at least getting yourself closer. So, if you're desperate, sit and wait if there are absolutely no cars, but once you see a car, always make sure you have your bag on your back, walk until a car gets close, at which point turn and follow above guidelines.
Do not walk away from a good hitch-hiking spot though! You are more likely to get a ride in a good spot where a car can stop, than in a bad spot, walking.
For obvious reasons, the less baggage the better. However, a backpack will clearly show your intentions and that you are traveling, while being completely empty-handed may look a bit suspicious.
In most European countries it is alright to hitch on smaller or secondary roads, but illegal and very unpleasant on highways.
If you want to cover big distances in a short amount of time, try long hauling. Place yourself close to the road or traffic light that leads up to the slipway connected to the highway.
Hitching is anything but an exact science but cars with kids and (mysteriously enough) campervans are tough crowds. Consequently areas full of tourists or holiday travelers are hard nuts to crack.
Any weather is good weather for hitching. A rainy day might just count in your favor because you look so darn miserable. An easily removable poncho may indicate to picky drivers their car won't get soaked.
Camping gear and some provisions are a good idea as you can never be entirely sure when and where your traveling for the day will end.
Be a nice hitcher. Attempt some conversation with the driver, it is often why they pick you up and you will probably learn something new and interesting about the area that you are finding yourself in.
Before getting into the vehicle, look directly into the driver's eyes. You may be able to tell if s/he has malicious intent. Use your judgment. Also, ask the driver where they are going, and while doing so smell for alcohol and look for safety issues with the car, such as no seatbelts, etc. If you don't like how it looks, smells, or you just have a bad feeling, tell them you want to wait for a ride that is longer or takes you to a better position. Just because they pull over doesn't mean you should get in. Above all, be observant of the driver and your surroundings.
Hitching as a couple will generally give you the fastest results.
The Hitchwiki has additional tips
Use Liftershalte.info to find good hitching places.
Always carry a towel as if a driver sees you with a towel (s)he will presume that you have other equipment. Eg. Toothbrush, food, water. Sometimes they may ask if you have enough supplies and may give you free food as a result.

[edit] Warnings

Many people do not consider hitching a safe method of transportation for good reason. If you decide to hitch, common sense is your best protection. Don’t hitch at night and preferably not alone. Have a map to know where you are going so that you know if you’re not. As with any trip, let friends know where you are and how you are getting along.
In some European countries the "hitchhiker's thumb" may be taken as an insult.
This may be illegal in certain states/provinces.