Surawee,
1.Can I buy a 1 day travel card in the day I arrive but I need to use (valid) in the next day?
You can use a card whenver you like. You have only to scratch the numbers (year, month, day) on the card.
You can also buy a card from tram/bus drivers.2.Can I use for both tram and city bus?
There're 2 types of 1-day card, "Ichinichi Joshaken (1-day pass)" and "Kagoshima City View Ichinichi Joshaken (Kagoshima City View 1-day pass)." Make sure that you'll buy "Ichinichi Joshaken." Kagoshima City View Ichinichi Joshaken only covers City View buses while Ichinichi Joshaken covers city buses/trams. (City View buses are tourist buses which circle around major tourist spots)
3.How can we use when I take a city bus or tram ?
You have only to show the card to the bus/tram drivers when you get off.
This site may help you;
http://www.synapse.ne.jp/~update/transport/transport-e....