In general, you can reach everywhere in Changhua quite easily by foot, unless you have a lot of luggage to carry. It is only a 15-minute walk, for example, from the University to dowm town.
The Changhua Bus company has an extensive bus network. Currently, a single bus trip costs about 22NTD. Tickets can be purchased from the bus driver or at the Bus station. The bus station is located right beside the train station. Here, you can also find the U-bus to other cities, for example, every one hour is a bus to Taipei for just 300NTD(one way).
You can get away from Changhua with Taiwan Railroad easily. Check the exact departure and arrival time of your destination from http://twtraffic.tra.gov.tw/twrail/English/e_index.aspx
Taiwan Railroad uses a simple system of train fares, no matter you are buying tickets on the internet or by the machine. It will not cost you more to buy tickets from the counter! It is convienient!