Linyi is relatively easy to get to by air with multiple flights daily coming in from Guangzhou, Shanghai and Beijing. At the airport you can take a taxi into the city, be warned the local drivers will try to bargain. The airport is extremely close by Chinese standards, best bet is to point to the meter and pretend you don't know any Chinese.
Linyi is relatively well connected by train with daily train services to Beijing, Jinan and Qingdao. Expect to pay approximately ¥120 for a seat each way to Beijing in the slow train, or ¥200 for a bunk bed place.
Linyi has at least two inter-city bus stations, most locals see to "show up" at the bus stations as there is no pre-booking system.