The standard route is by road from Kisumu, 65 kilometres south. Matatus on the Kisumu-Kakamega route run every twenty minutes or so during daylight hours; the journey takes about ninety minutes and costs a few hundred shillings. From Nairobi, the easiest options are an overnight bus (about ten hours via Nakuru and Kisumu) or a domestic flight to Kisumu followed by a matatu onwards.
Once you are in town, both forest stations are accessible by matatu plus a short walk: Buyangu on the northern side via the village of Shinyalu, Isecheno on the southern side via the village of the same name. The matatus stop at the main stages in town; ask for the right route at the bus park, where touts are abundant and not always honest about prices. A taxi to the forest from town is around 1,500 shillings one way and may be worth it if you are travelling with luggage.