The tunnels were dug with simple tools and bare hands during the French occupation in the 1940s, and further expanded during the Vietnam War in the 1960s to provide refuge and a defensive advantage over the American soldiers. Despite all the bombings in their town, the Cu Chi people were able to continue their lives beneath the soil, where they slept, ate, planned attacks, healed their sick, and taught their young. Some even wed and gave birth underground, but over 10,000 lost their lives here.
A multitude of tour buses leave Ho Chi Minh City for the Cu Chi tunnels daily and can be booked by any tourist office. Expect to pay around US$5 (as of January 2014) for a half day guided trip to the Ben Dinh site (not including admission to the tunnels), with 90-120 minutes travel and about 90 min touring the area. Buses mostly leave around 8:00, so consider a private car if this isn't suitable or if you want to go to Ben Duoc instead. Tour operators on Pham Ngu Lao will quote from $45-75 return by private car, or possibly lower -- don't be afraid to shop around.
If you're making the trip independently, hop on bus 13. It leaves from the BẾN CV 23/9 bus station (between Lê Lai and Pham Ngu Lao, western end) and you can catch it along Cach Mang thang Tam. Just look for the bus stop signs with Route 13. The last stop on the route is Cu Chi. Bus fare is 7,000 VND, and the ride is about 1.5 hours. When you arrive at the Cu Chi bus station negotiate a motorbike driver for the 20-minute ride for around 100,000 VND return (pay attention as starting price could be 200,000 VND or more). It is also possible to take bus 79. Ask the driver for Cu Chi tunnels, the ride will last about 45 minutes and cost 6,000 VND. The bus will reach a T-junction with Ben Duoc on the left and Ben Dinh on the right. Get off at this point and walk on to Ben Dinh, or stay on the bus as it drives right pass the Ben Duoc entrance. Warning, the buses are sometimes very warm and crowded but manageable.
Admission to the tunnels at either Ben Dinh or Ben Duoc is 90,000 VND as at January 2014 which includes a guide who may or may not speak English well. While friendly, these guides may attempt to rush the tour or distance you from paid guides/groups -- just indicate that you aren't ready to move on yet and take your time if you feel you're being rushed.
Many guidebooks and tour information fail to indicate that there are actually two different tunnel sites open to visitors, operated by the same organisation and with similar experiences in each (a 15-minute scratchy B&W propaganda film, tunnel tour, displays of booby traps, tasting of tapioca):
This is the less touristy and original tunnel and can be reached easily by bus 13 and 79. Bus 79 stops right in front of the tunnel entrance. Consider this over Ben Dinh if you want to avoid the crowds.
If you drive to Ben Dinh on your own you find the real coordinates to the tunnels here (as the coordinates shown on google maps are obviously wrong and there are very little signs directing to the tunnels): 
There is a bus from Cu Chi to Tay Ninh: Bus no. 70 -1
From Cu Chi – Tay Ninh: Cu Chi station – Highway 22 – Trang Bang station – – Highway 22 – Go Dau Tay Ninh station.
At each site (Ben Dinh and Ben Duoc) a well defined walking track loops around the area, with things to see spaced at regular intervals, including examples of how people lived and what they ate. There are sample sections of tunnel which visitors can crawl through (not recommended for the claustrophobic), examples of traps used during the war, and the remnants of bomb craters. Warning: Many travellers put themselves into small ventilation holes for phototaking. It is great fun but consider your body before getting in as some had difficulties getting out and had to crawl to the exit point.
There are numerous souvenir shops at the end of the walking track. Given the location there is some focus on war memorabilia, as well as the traditional Vietnamese souvenirs found elsewhere.
There are a number of stalls selling food and drinks near the entrance. Mid-way around the walking track is a kiosk/restaurant selling drinks and food and ice-cream at reasonable prices, and at the end of your tour there are samples of traditional boiled tapioca to try.
You can also rent a room in any hotels in Ho Chi Minh city stay and visit Cu Chi tunnel in one day. After that you can return to the downtown and enjoy your night in the lively atmosphere.