Three Days in Beijing
While more or less everything can be obtained or arranged on the spot, you should nevertheless prepare a little.
Wangfujing (王府井大街 Wángfǔjǐng Dàjiē), (Subway line 1, Wangfujing station). Beijing's most famous shopping street, nowadays with mostly the same international brands and modern malls you will find anywhere else in the world.
Fortune favours the prepared mind
See the main Beijing article for information on how to get to Beijing and how to move around within.
Other than the Great Wall, most of this itinerary can be covered on foot, with few subway rides to starting points and back. However, distances in Beijing are generally far, and some may prefer taking a taxi for parts of the itinerary. See the main Beijing article about how to get around in the city.
If day one is your arrival day, the morning will probably consist of getting to the city from the airport, finding your accomodation and getting settled. If you do have the time, the Temple of Heaven is a good place to start the day.
After getting settled, head to Tiananmen Square and enjoy the huge plaza with its grand buildings, socialist monuments, and the portrait of Chairman Mao above Tiananmen gate. The square can easily be reached by metro line 1, stations Tiananmen East or Tiananmen West. Alternatively, take line 1 to Wangfujing street for a quick bite of lunch and then walk over to Tiananmen (south on Wangfujing, then west on Chang An street)
Head north from Tiananmen Square through the famous red Gate of Heavenly Peace and on towards the Forbidden City. The huge Palace Museum (i.e. the forbidden city proper) is one of the Beijing must-sees, and thus fairly crowded and expensive (admission ¥60, local or foreign students ¥20). Stroll through the magnificent area and explore some of the hidden courtyards. Budget about two hours for the whole area, possibly more if you are really into it or want to see the extra exhibitions as well. Keep walking in a general northerly direction and you will end up at the exit on the opposite side.
From the north end of the Forbidden City head West to Beihai Park (10 minutes walk along the Forbidden City moat, some beautiful views). Beihai Park (admission ¥25) has a nice lake and a central hill with the White Dagoba that can be seen from afar. Enjoy the nice green, and the ample opportunities for a snack before climbing up the hill to the Dagoba. Exit Beihai on its east end.
From Beihai Park simply go east to the next Park, Jingshan (admission ¥10, local students ¥5), which is at least as beautiful as Beihai, though not as big. Climb the hill for some great views of the Forbidden City as well as the rest of Beijing. The flora in the park is also beautiful. This may also be a good place to see the sunset.
If you are still not too footsore, head east from Jingshan and straight into one of the narrow Hutong areas (e.g. at Jingshan Dongjie), and keep going east until you come upon the next major road, Beiheyan Dajie. Parallel to this runs a narrow strip of green park due south. Enjoy the park for about half an hour's walk until you come to Dong'anmen Dajie, and go east for one more block to the Donghuamen Night Market.
Conclude your first day in Beijing with some tasty snake or scorpion at one of the stalls, or have some other more 'mundane' dinner in one of the restaurants.
Day two is when you get to see what you have most wanted to see, the Great Wall. Check out the special article about the wall, and also have a look at The Great Wall Forum, which has many helpful tips about many sections of the Wall and how to explore them.
It's easiest to simply book a guided tour to the wall, but be sure to do it at a reputable travel agent or the tour desk at your accomodation. There are many, many rip-offs and crappy tours. Specifically, you should make sure that your tour contains no shopping or other unwanted time-wasters. Many tours also include a trip to the Ming Tombs.
If you are a little adventurous and want to see a part of the wall that's (much) less frequented and also less restored, take a tour to Jinshanling. While that's about a three-hour drive one way, you will be treated to many breathtaking views and a chance to take a long hike with very few people around (maybe about 2-3 tour buses for the whole day, mostly Western folk since hiking is rather uncommon in China). Tours are about ¥230 with two meals, plus ¥50 entrance fee. If you are fit, there is no need to spend another ¥50 on the cable car, as the wall can be reached in about 15 minutes on foot.
If you decide to take a tour that doesn't last the whole day, you might also consider checking out the Ming Tombs or the Olympic Park in the afternoon.
An event that is seemingly quite popular among domestic tourists, but much less so among foreigners, is the Flag Ceremony at Tiananmen Square. If you feel like, get up early enough and make your way to Tiananmen Square (also a nice opportunity to see Beijing rather deserted) before sunrise. Try to be a bit early if you actually want to see the ceremony through the crowds. The whole event, however, takes less than 15 minutes and the crowd is rather intent on taking many pictures as opposed to cherishing this solemn patriotic moment.
After this early start, you may want to crash at your accomodation for another hour or two, or find some place to have coffee and breakfast (most of Wangfujing St is closed, though, except some McDonald's and KFC places). Once the stores open, take some time to shop for souvenirs before the crowds start pouring in.
Later in the morning, resume sightseeing at the Lama Temple (Yonghegong), which you can easily reach by metro line 2 (take the south-east exit). The temple (¥20 admission) is a fairly big complex with several gates and halls with countless buddhas and other figures. The largest of the statues is at the very back of the temple, an 18m buddha figure that fills a large building up to the ceiling. The place shouldn't take more than an hour to explore.
From the Lama Temple head west (only a few hundred meters) until you reach Confucius Temple (¥25 admission, student discount available), which is much more quiet compared to where you have just been. Be sure to also check out the adjacent academy (first gate on the left, after you enter by the main entrance), which is even less frequented and also boasts some richly decorated beautiful halls and beautiful reflections in the small moat.
Continue heading west from Confucius temple and you enter one of the more popular Hutongs (=traditional neighborhoods with narrow alleyways and winding lanes). This is a great area to explore just randomly, and also to have some coffee or a little lunch. Try not to get lost, as it is very easy to walk in circles and those tiny streets are not to be found on any map.
Heading west you finally arrive at the last sight of your trip Drum and Bell Towers (near Gulou Dajie), which are again popular among tourists, and thus slightly crowded. Once you have had enough, you can catch the metro at Gulou Dajie station (10 min walk north of the towers). Depending on how and when you started the day, it may now be around 2:00-4:00pm. Don't miss your plane.
Stay away from touts offering rides on three-wheeled vehicles.