Until about the mid 1950's Giessen had actually trams and after that trolley buses but these day it's just buses. If you don't want to walk to the center take a bus to ie "Marktplatz" as most sights are within walking distances from there.
Giessen is less than an hour from Frankfurt/Main by regional train and is a crossroad for various train lines, although you will not find ICE trains here. The old station looks pretty from outside. In the station you will find lockers, a newsagent and snack shops and of course a ticket office.
On the station concourse there are taxis and buses. On the pavement opposite the station you find a map of Giessen.