Regular buses and trains run from Riga to Sigulda. The trip by train should take about an hour and 15 minutes. The bus goes along the highway outside of town so ask the driver for the Sigulda stop. The train station is right in the centre of town.
Shuttle buses connect Sigulda, Turaida and Krimulda, none of which are more than 5km apart. They run about every 30 minutes - check with Tourist Information for exact schedules. For maximum fun with minimum risk, take the cable car from Sigulda to Krimulda. The trip takes you over the Gauja river valley in less than four minutes.