Originally it took a 5 hour climb up the mountain to get to the Temple but thanks to 1,000 volunteers who built the current road the journey now only takes about 40 minutes. The best way to go up is buy flagging down a red Songthaew truck taxi. If you are only going to the main Temple and back it will take you about 40-45 minutes each way from Chiang Mai and will cost 200 Baht around trip. We recommend hiring a taxi for a full half day to take you to all the site which will cost 400 Baht for an open Red Songthaew Truck Taxi or 500-600 Baht for a Cat Taxi. Either option will wait for you while you look around and you pay at the end. Overall getting to Wat Doi Suthep Temple is easy and cheap.
If you wish to have a tour guide the whole time, tours like this one stop by the Temple and Hmong Village on 4 hour trip for about $50 a person. A little more high end guided tour, listed here, goes to Doi Suthep Temple, Tiger Kingdom, the 5 Hill Tribe village, and to 2-3 of Old Towns major Temples one an all day trip for $75.