Wamena itself is walkable. To reach villages around the valley, share bemos (minibuses) leave from a Wamena terminal for the main settlements — Jiwika and Kurulu to the north, Hitigima and Sugokmo to the south. Fares are very cheap; expect to wait for them to fill before they leave.
For multi-day treks deeper into the valley and over into the Yali country to the east, hire a guide and porters in Wamena. The standard rate is per-day plus food. Independent trekking without a guide is technically possible but not recommended — paths braid, weather changes fast, and villages may not welcome unannounced visitors.