Taxis
Taxis within the city of Baños usually cost a dollar. If you are going far, like the zoo for example, it´ll be aprox. $1.50.
Buses
There are buses to/from Quito aproximately every half an hour, from 4 in the morning till 12:00 midnight. The drive is aproximately 3.5 hours.
There are buses to/from Ambato every 5-10 minutes (1 hour drive).
To get to Cuenca, you´ll need to take the bus to Ambato first, and then transfer to a bus to Cuenca. The bus from Ambato to/from Cuenca leave apromximately every 1.5 hours.
Buses to Guayaquil leave at 7:00am, 1:00pm, 5:30pm, 7:15pm, 11:00pm, 0:15am, and take about 7 hours to arrive. You should make verify that there is actually a bus at the time you want to travel.