The railway and bus stations are close to each other a few min on foot east of the city centre.
If you arrive at the Beauvais Airport, then it's easy to get to Amiens by bus. There is a shuttle bus to use. Here is the link to the bus company.
The bus service at Amiens is called Amétis.
I found their maps and routes
You may find these links handy:
Tourist office: http://www.amiens-tourisme.com
Bus maps: http://www.ametis.net/ftp/FR_plan/PLAN%20CLIENTS%20SEPT%202008.pdf
The best way to get to Amiens from the North is to take a train from Lille. It takes about 2 hours due to stops. The cost is around 8-10 Euros. Information on France's trains can be found at www.eurostar.com.
From Paris you should take the train from the Gare du Lyon, trains leave for Amiens about every two hours. It takes about 2 hours from Paris due to stops in Creil, and other paris suburbs. The cost is around 8 Euros for ages 12-26.
Finally, if arriving at Charles de Gaulle airport, you should take the 'Yellow bus'. This bus comes about 5 or 6 times a day and takes you straight to Amiens. Excessive baggage is not a problem. The website for the Bus jaune is www.busjaune.com. There you can find schedules, prices, etc. One problem: the terminal at the airport is really hard to find!! When I first arrived at the airport and was told I needed to find terminal F2 I had no clue where to go. The people who gave me directions were none too helpful either! I finally realized that to get to this pickup spot, you must take a transport bus to another aerogare and then take an elevator to the basebemt where you'll find the bus terminal. Very confusing! I'd suggest going with a detailed map of the airport.
The best way to get around the centre ville of Amiens is to walk. The downtown walk areas and one way streets aren't really condusive to driving. Your best bet in finding your way around is simply to walk around the many streets. You can see much more and soak up more when you're slowed down enough to actually enjoy the city. Plus, every where leads you to either a pretty square or the Cathedral. How can you go wrong? The bus system is also really good in Amiens (that is, when the workers are not on strike...). There are 6 lines if I remeber right. Combined, these lines go to every corner of Amiens. The fare is usually one dollar each time you ride, or you can buy a packet of bus tickets at any of the tobacs. These usually come in packs of ten and cost around 7 dollars. The Gare du Nord is the transfer site for all lines.
Being so close to Paris, Picardie is very accessible from the rest of the world.
If you just want to make day trips from Paris, use the public transportation. It is cheaper and very efficient. If you prefer to drive, roads are very good.