There is a bus that goes to the Great wall but you have to transfer several times and its a long trip. That's one way to go there on your own. If you want to take the tour just find those people passing out flyers and book a tour with one of them.

To do it right, you should invade from the north with a few thousand Mongolians...

if not...there are tours. I went to Mutianyu with a youth hostel tour. They drove us there in a bus, hiked 10km, then picked us up at the end from a restaurant where we ate lunch (included in the price)

I think it was with the Jade Youth Hostel.

Mike, the Great Wall is like  snake laying on the ground but a few thousand kilometers long, so it (8,851.8 Kms long) would depend where exactly you wish to intersect it.  You mentioned going to Beijing, and yes, that could be one way.  Now, it may be easier to try to book a day tour from whichever hotel you will be staying at, or a nearby travel agency.  But you must be careful to where within the Great Wall you will be taken, some areas (like B   ) are more popular (and thus crowded ) than others.  Also, it ould be a good idea to combine the trip to the Wall with other nearby tourist areas, like the Summer Palace and the Underground Tombs.

When I did this, I recall the guide I used took me to see what it looks like a stone old bridge over a creek.  I was there with an expression on my face saying "WTF is so special about this stone bridge"?  Well, in his broken English the fllow took me to a spot on the bridge, and took my photo.  Afterwards, he explained that Marco Polo used that bridge to invade Beijing, and there was a painting of him standing where I had stood.  So, sometimes taking a guide will get you a ittle extra.

Now, if you do not take a tour, and wish to go by yourself,  please find below a schedule showing bus number, schedule hours, cost and time of traveling to different sections of the Great Wall.

Badaling Great Wall
Deshengmen Gate is a transportation node in Beijing. Lots of buses depart from here. Bus 919 is an public bus which drives to Badaling. Badaling is the most popular part of the Great Wall and in high season very crowded. There are two 919-buses. One bus stops more near the Great Wall but has more stops along the way (8Yuan, 1,5 hr). The other 919-bus is faster (12Yuan, 1hr) but you have to walk 15 minutes longer to the ticket office. The 919-bus is running between 6.30 and 12.00 from Deshengmen to Badaling. Departure from Badaling to Deshengmen is from 12.00 to 17.00. Beware that you don't take a private bus on Deshengmen. Fares for these private buses are much higher. (they can charge you hundreds of Yuans for a ride).
 

Train to the Great Wall
The train leaves from Beijing North Railway Station at 06:08, 07:26, 08:00, 09:33 and 10:20. It is one hour to Badaling. Fare is around 15Yuan. The entrance of the Great Wall is nearby the station.

Beijing city bus
City buses are cheap (1/2Yuan) but often very crowded
buses 1 – 122 : Beijing downtown
buses 300 - 950: Beijing suburbs
bus 330, 331, 332, 346 to the Summer Palace
bus 17, 35, 120: Temple of Heaven
bus 9, 10, 20, 24, 25, 39, 52: Beijing Central Station
bus 1, 2, 4, 5, 10, 20: Tiananmen Square
 

Beijing long distance bus stations
Bawangfen Long-Distance Bus Station, Chang'an Avenue (Tianjin, Baotou, Shenyang, Dalian,Changchun, Harbin)
Liuliqiao Long-Distance Bus Station (Zhengzhou, Hohhot, Dalian)
Muxiyuan Long-Distance Bus Station, No.199, Haihutun, Fengtai District (Nanjing, Jinan, Hangzhou, Wenzhou)
Sihui Long-Distance Bus Station,No.68, Jianguo Lu, Chaoyang District, (Changchun, Chengde, Dalian, Liaoyang, Tianjin) Xianglong Zhaogongkou Long-Distance Bus Station (Harbin, Tianjin, Chengde, Shanghai)
Zhaogongkou Long-Distance Bus Station (Cangzhou, Jinan, Tianjin)

Jinshanling Great Wall
Simatai Great Wall
Take bus number 980 from Beijing Dongzhimen Long Distance Bus Station to Miyun County. In Miyun downtown take the local bus to Jinshanling Great Wall.
Bus is running between 6.00 - 18.00. Bus Fare 10 Yuan. Mini Bus fare 10 Yuan.

Mutianyu Great Wall
Take bus number 916 from Beijing Dongzhimen Long Distance Bus Station to Huairou Distric. Take the mini bus from Huairou to Mutianyu Great Wall.
Bus is running between 6.00 - 20.00. Bus Fare 12 Yuan. Mini Bus fare 40 Yuan.
 

If you go to the Tiananmen Square where the subway is they just added a big sign to show foreigners or whoever is interested in going to all of the best sites in CHina how to get there. I remember reading the one about the Great wall the direction was pretty easy you have to take one of the lines forget if it's line 10 or 2 then you have to transfer I think one time. Anyways if you have a chance to go to Tiananmen there is a sign under the subway I know I was there yesterday and saw it. Plain as day and the directions how to get to each hot spot is listed on a big sign you can't miss it trust me.

go to a hotel that organize trips most all do