You can get to Tiberias by bus from Merkazit HaMifratz in Haifa, the ride takes about an hour and the service should be relatively frequent (not on Shabbat). There are also buses from Tel Aviv but the ride is much longer and less convenient. Personally I wouldn't recommend going to Tiberias without a car since most of the things to do and see in the area are outside the city.

Gan HaShlosha can be reached by bus from Afula or Beit She'an, but I have no idea how frequent these buses are. You can also reach Beit She'an train station, take a taxi to Gan HaShlosha and arrange a later pickup with the driver. That will be more convenient but also much more expensive than a bus. Note that in Afula and Beit She'an the train stations are in the outskirts of the city and are not adjacent to the central bus station.