By ship
Boats from Nusa Lembongan arrive at the beach at the end of Jalan Hangtuah, and detailed schedules are given in the Nusa Lembongan article.
By car
Sanur is a 20 minute taxi ride from the Ngurah Rai International Airport, and a pre-paid coupon costs Rp 95,000. There are plenty of metered taxis all over the island who will be keen to take you to Sanur.
If you are driving yourself, this is one of the more staightforward areas of Bali to find as the main Jalan Bypass Ngurah Rai is the western boundary of Sanur. There are many well signposted exit points from this main road into the heart of Sanur. Allow about 20 minutes driving time from Kuta or Legian, about 30 minutes from Seminyak or Ubud and 10 to 15 minutes from Denpasar.
By bus
Sanur is well serviced by shuttle buses and bemos from the north and south and also from Denpasar's Tegal terminal. The bus company Perama (http://www.peramatour.com) has its Sanur office in Jalan Hangtuah, and offers difrect transfer here from Candidasa, Kuta, Lovina, Padang Bai and Ubud. Private shuttle buses run from most major tourist centres of Bali to Sanur; check local advertising and always book 24 hours in advance.
There's also a free bus service called Trans Sarbagita that runs following route Term. Batu Bulan Gianyar - Tohpati DPS - Sanur DPS - Kuta Central Park Badung - Jimbaran Badung - Nusa Dua Badung. It's free till 31st of August 2012 as per government funded program.