There are two bus stations in Jinan.  The first one,

Through Transport Bus Station (汽车联运站)

is across the street from the main train station.  In fact, when you exit the train station, the bus station will appear exactly as pictured above.  There is a little ticket booth to the right of all the buses, but usually you can go right up to the bus and the ticket checker will handle it for you.  Knowledge of the Chinese characters of your desired destination is useful, or at least the ability to pronounce them (as best as you can).  These buses are not city buses.  They will take you throughout the province.  City buses can be caught to the right of the bus station heading south onto Jing Yi Road. Tel: +86 (0)531 8594 1472

and then there’s the Long Distance Bus Station (济南长途汽车总站)

located at 131 Ji Luo Road (济泺路131 号).  There’s an information desk inside which, on a good day, has English service available.  Most buses that arrive in Jinan will drop you off here.  Just outside the station there is a major local bus stop on the right side. From here  buses can take you anywhere in the city, though Chinese is more than recommended for travel by bus.  +86 (0)531 8691 0789

There are two train stations in Jinan. 

The Main Railway Station

The main station is located near the intersection of Wei Er (纬二) and Jing Yi (经一) Roads.  It is, in fact, on its own special street, called Train Station street (火车街)。  One of Jinan’s two big bus stations is directly across the street from the station, offering bus service to Qingdao, Mount Tai, and other provincial tourist destinations.  Pictured above is the ticket office.  Once you’ve purchased your ticket, head through the next large entrance to the right of the ticket office to find the waiting rooms.  Look on your ticket stub for the train number (it might be preceeded by a K, T, or N), and destination. Then use this information to find the number of your waiting hall which is listed in red on signs hanging from the ceiling.

Local buses are just 50 meters from the train station. Exit the station and head to your right. Follow the road a bit and stand with the people with luggage in their hands.  Bus K51 is one of the many buses that goes to the bus station.  It is air-conditioned and travels southeasterly in the direction of Thousand Buddha Mountain.

You can, of course, buy train tickets at the train station (I recommend buying tickets at least three days in advance). However, closer to Thousand Buddha Mountain, is one of many auxiliary ticket stands.  For a very small commission auxiliary ticket agencies will book train tickets 5 days in advance, and can also book domestic flights for you. 

Long Distance Rail and Air Ticket Center  ("Train Tickets" is in English on the sign outside)
方远铁路航空票务中心
No. 74-1 Jing Shi Road (经十路74-1号)
+86 (0)531 8822 4419, 13210596327

Jinan East Station (济南东站)

Jinan East Station is located just north of Minghu Bei Lu (明湖北路).

Buses 6 and 122 stop right at the train station.  Buses 83, 118 and 201 stop on Minghu Bei Lu.  Several other buses stop within walking distance of the East Station.

The exit of Jinan East Station.  The entrance and ticket booths
are to the right.

Link: More information on taking the train in China.

To get to the airport, take a taxi for about 100 yuan to or from.  Make sure you agree on the price before getting in the cab.    The taxi driver will ask you whether you want to go on the expressway (Gao Su Gong Lu) or not.  It'll be ten or twenty yuan if ou do. 

Or you can take any one of the airport shuttle buses going to and from major hotels in Jinan.  Just pretend you'll be a guest and pay a small fee, usually not exceeding 20 yuan, and you're on your way.  Once in the city, take a local cab to your destination starting at 7 yuan.  Major Hotels include the News Hotel, the Hanlin Hotel, and Sofitel.

You can book international and domestic tickets here, however I'm sure you'll pay top dollar doing so.  Try a travel booking service, for example

Shandong Travel Agency (山东旅行社)

201 Shan Da Road, Li Xia District (历下区山大路201号)

(0531) 86590186

Official Website (Only in Chinese)

For Domestic ticket: +86 (0)531 96888
For Internation ticket: +86 (0)531 8185 0000