San Agustín is a UNESCO World Heritage Site.
From Bogota you can take a bus, the way is safe and there are beautiful places to see like the Magdalena River, the most important of Colombia.
There are several direct busses from Popayan to San Agustín, it's a long 7 hour bus trip on unpaved road.
If you go to Tierradentro take a bus to Pitalito. From there you have to take a bus to La Plata either at 6AM or 10AM. From there you can make connections to Tierradentro.
There different archaeological sites are scattered over a large area. If you have the time walking is the best option, the scenery on the way is amazing and some of the local transportation can help you on your way. It is also possible to rent horses. Several agents run jeep tours to some of the more remote sites.
Besides the archaeological sites there is some beautiful nature to visit.
There are ATMs in San Agustín, buy they are not very reliable. To get money you may have to go to Pitalito. Bring your passport or you might end up in the DAS office in Pitalito. The only ATM in town does give cash advance on VISA credit cards.
Finca El Maco. Run by an extremely friendly Swiss (Rene) and his wife (Paloma) Finca el Maco is a little piece of paradise located about 1km out of the town of San Agustin on the way to the archaeological site. Dorm beds and private rooms are available from 14,000 Pesos pp and there is also a restaurant and bar which serves incredible meals.
La Casa Francois - Beautifully set in the countryside, a short walk from downtown. Beautiful views, exquisite breakfasts and dinners prepared by request. Both dorm and private rooms available. Excellent backpacker hangout with all of the amenities.
Finca El Cielo Very beautiful farm at three km of San Agustin near to fascinating archelogical sites. Owned by a Swiss (Dominique) and run by a friendly Colombian family. Beautiful views over the Magdalena cañon. Ample and very comfortable rooms with modern bathrooms. Swimming pond. Camping. Tours. 
Most guidebooks may tell you this area is guerrilla territory, but this is no longer the case.
Some of the agents organizing jeep tours are more interested in your personal belongings. Set up tours at your hostel.