Sumba has airports at Waingapu and Tambolaka, both of which have daily flights to and from Denpasar, Bali and Kupang, West Timor. Check tiket.com for fights and booking.
Pelni (Indonesia’s national shipping company) operates a passenger service stopping in at Waingapu twice fortnightly, coming from Bali and Lombok, then continuing eastward to Flores. It’s a good way to get to Sumba but if you’re planning on returning back to Bali or Lombok, it’s not really a practical way to get off the island. Keep in mind that schedule and route changes do occur, so check the Pelni website (you’ll need to use the Google Translate option) for the latest information.
Alternatively, there are more frequent local ferries and small boats linking Waingapu, Waikelo port near Tambolaka and some smaller Sumba ports to Flores, Sumbawa and Kupang. You’ll need to make inquiries at the local wharf a day or two before you want to travel.