In the Cinque Terre National Park, the protection of the environment is of high importance so you can travel only in an environmentally friendly way in the villages. Besides trains and boats, electric buses are used, which run between the coast and the villages and sanctuaries higher above the hills.
You can use these buses free with the Cinque Terre Card, otherwise one ticket costs 2.50 EUR if you buy it on the bus and 1.50 EUR if you get it at the tourist information centers of the National Park. I think it is worth getting on these little buses: you can get to some smaller, quieter villages, like Groppo and Volastra, or you can visit some hidden churches. On the coastal road, where the buses run, you can enjoy an amazing view over the sea and the terraces. The drivers are usually local guides as well so they might tell you about local life and answer your questions.
In some villages, you can take the bus from the parking area to the center if you wouldn't like to walk a few minutes. In Corniglia, you can get by bus to the village center from the train station.
Please ask the Information Centers of the National Park for schedules.
The combination of taking the bus and hiking is also a good way to discover the national park if you don't like tiring uphills. It is nice to walk down from the Telegrafo to Riomaggiore. Another great option is taking the bus from Manarola to Volastra, then hiking from Volastra to Corniglia. You could also take the bus from Vernazza or Monterosso up to the sanctuaries and walk down from there. From Vernazza, just take a roundtrip with the bus to enjoy the great views. The view of Vernazza from the top of the hill is one of my favourites in all of the Cinque Terre. Although the drivers generally stop at the lookout point for a quick photo stop, it's always better to ask them. The buses are usually used by locals living further up the hills.
There is now a brand new bus service called "Explora 5 Terre" connecting the villages and some hamlets of the Cinque Terre. This small bus can be a very nice alternative to the crowded trains, especially that the views from the road are stunning. The buses have 22 seats, they have A/C and your driver will give you a small map of the route and the villages. The buses run between 8:30AM and 10:00PM, every day of the year.
At the moment the bus cannot go to Monterosso, as the road between the two villages is closed. On certain days the bus also stops in La Spezia at the cruise terminal.