Talsi is small town, so you can walk from one side to another in less then 30 minutes. There is very good public bus system all around Talsi distric and among other regions. There is even bus circulating around the town during the day.
The only problem can be if you are coming from Riga and the driver leave you on A10 just before exit to Talsi (most drivers are doing so as they are heading to Ventspils). Best idea is to walk by the road to the Talsi direction (on right) and start hitchhiking again just after U get of the exit (it is ~300m long).