The Beijing Subway is continually growing and stretching farther and farther out of the city. This of course means it is even more crowded than when it was smaller, but the vast distance can be covered for a mere 2 RMB (30 cents) per person. Free under 1.2 meters. It is also fast and dependable no matter what time of day. Rush hour is still best avoided but nevertheless most people will offer children or the elderly their seats.
A downside is some Beijing Subway interchanges require a lot of walking, so bear that in mind with younger children. And while most exits have an escalator going up, most do not going down and there may be only one exit (if that) with an elevator. You can download an English Beijing Subway map for smartphones.
Likewise, public buses in Beijing can you take you quite a long distance for even cheaper. Many for 1 RMB, or a few more if paying cash. If you have a subway card, you can go almost anywhere for less than 1 RMB. The upside compared to the subway is there is no going up and down and you can see outside and buses can take you closer to your destination.
The downside is, while Beijing Subways are all clearly marked in English, bus stops are not. You will need to know in advance the name of the stop and how to read it in Chinese or have researched online which bus number and when to get off. The official bus site is only in Chinese, but using map apps like Google you can see the bus stop names and some of the bus numbers that stop there. Or use an English site like travelchinaguide.com and put in the stop names in pinyin or bus number and see the route options.