Riga - Cesis is about 90km... The bus is the easiest way to go there... Just go to the bus station and get a ticket... :)) Buses leaves from the Platform 10 every hour and sometimes also more often... Just check it out at the station or by calling to 118 (infoline)
There are few daily train services to/from Riga (2 hours, 1.50 LVL), Sigulda (less than 1 hour; less then 1 LVL) and Valmiera (half an hour; 0.50 LVL) and Lugazi near Valka (more than one hour; more than 1 LVL). More about it here: http://www.1188.lv/satiksme/vilcieni/.
There are regular bus connections to/from Riga (each hour or half an hour; 2 hours; 2 LVL), Sigulda (each hour or half an hour; less than 1 hour, 1 LVL), Valmiera (each hour, less than 1 hour; less than 1 LVL) and some other places. More about it here: http://www.1188.lv/satiksme/?sub=autobusi&lang=en.
If you prefare this kind of travel, just take the trolleybus NR6 till the Jugla (end stop) it will cost you 20 santims and just in front of you you will see many of the other people who has the same idea in their heads...
A TIP : write before on the paper CESIS with large letters and keep it in front of you because not everybody goes there and not everybody speaks English...