From New Chitose Airport
Take JR Hokkaido's "Rapid Airport Train" (快速エアポート) for Otaru. The services are available every 30 minuets by day. It takes about 1 hour and 10 minutes from New Chitose Airport to Otaru. Fare (one way): ¥1,740 (New Chitose Airport - Otaru)
From Sapporo (by JR)
In addition to rapid trains above, there are frequent local train services between Sapporo and Otaru in Hokkaido. It takes about 50 minutes by local train. (30 minutes by rapid train) Fare (one way): ¥620 (Sapporo - Otaru)
From Sapporo (by Bus)
There are also frequent rapid bus services operated every 5-10 minutes between Sapporo and Otaru. Take "Kosoku, (or rapid) Otaru" (高速おたる号) bus from Bus Terminal located in ESTA building in front of JR Sapporo Station South Entrance side. The buses have two routes to Otaru, via Maruyama (円山経由), and via Hokudai (北大経由), but traveling time is almost the same. It takes about 50 minutes from Sapporo to Otaru. You can also take Kosoku Iwanai (高速岩内) buses to Otaru.
The bus leaves from No.1 gate of the terminal. The entrance to the platform is found in the basement of ESTA. Fare (one way): ¥590 (JR Spporo Station - JR Otaru Station)
For the bus depot, see the following map.