Super Jet has daily speed boats carrying passengers from Tanjung Pinang at Bintan island to Dabo at Singkep island with stop-overs at Cempah Island and Jago (at northern part of Singkep Island). There is only 1 boat per day leaving Tangjung Pinang at 11.30am to Dabo, and the return from Dabo to Tanjung Pinang leaves Dabo at about 7am. The return journey should cost about US$15 and each journey takes about 4 hours! There are also other speed boats but not on a daily basis, there is one from Tanjung Pinang to Jago and then to Daik (Lingga Island). The views from the boat are very nice and the photos are at the travelogue section of this VT page.
PT Sabang Merauke Raya Air Charter (SMAC) is a small region airlines which offer flights from Batam island's Hang Nadim airport to Pulau Singkep via Bintan island. The fight from Batam to Singkep is three times a week (10am on Tuesdays, Fridays and Sundays) and flight time is about 1 hour. Return flights from Singkep to Batam are at 11.30am on Tuesdays, Fridays and Sundays (the same plane is used). The plane is a small one and can seat about 20 people. Cost is about 300,000 Indonesian ruppiah return (about US$40). There are no flights to Pulau Lingga, you have to fly to Pulau Singkep and then take boats to Pulau Lingga.
Flights offer the fastest way to reach the Lingga Islands and the views are spectacular (see travelogue section of this VT page for more photos taken from the plane). More detailed information and photos are the the transportation section of my VT Pulau Singkep page.