Form Forli, get a taxi to the train station -short trip so shouldn't cost much.
Then buy a ticket either from the ticket office or from one of the automated systems (in one of 6 languages!) to Bologna. It's one train, no changes required. Cost is 6 euros for the slow train (lots of stops) and takes about 1 hr 15 mins, or go for the Intercity option that takes 35 mins and costs 11 euros. Sometimes (in summer) the Intercity trains get fully booked so you have to stand - at busy times I recommend getting a reserved seat. This time of year shouldn't be a problem.
Full Italian train timetables are available online at
http://www.trenitalia.com/en/index.html I've used the Italian trains when on holiday in Northern Italy many times without a problem. They're exceptionally good value when compared to BR and generally run on time. Since Forli to Bologna is on a main route, you should have any problems with getting a train to suite your needs.