The easiest way to Waingapu, Sumba is via Bali or Kupang (Timor), by air or sea. From Waingapu you can easily find ride to each resort. Especially Hotel Merlin in town is reliable in organising transportation.
By air to Waingapu:
Merpati
1-2 flights a week from Bali and Kupang. One-way ticket approx. $80(USD).
Link: Merpati website
Pelita Air
Four flights a week form Bali. One-way ticket approx. $80(USD)
Link: Pelita Air website