I live in Sweden, I'm sure some rules are different such as how much taxes you have to pay and so on, but basically I'm guessing it's the same.
I have ordered game-stuff from the internet a couple of times with varying results. You may have to pay extra tax - the shops do not have this on the price already since the taxes differ from country to country.
I have not spotted any certain pattern as to when one has to pay tax and not, so I think it mostly comes down to if you're lucky or not. If the shipping is with FedEx, DHL or similar they will pay taxes for you and bill you later.
When I ordered Star Wars: Galaxies from dvdboxoffice, I had to pay tax. When I ordered a Nintendo DS and some games from importmadness.co.uk, I did not have to pay tax even though all the paperwork suggested it had gone through customs openly, ie should have been taxed.
And ordering from people on Ebay I have never had to pay tax.
I have preordered Psychonauts from EB games and I got a mail from them asking me the name of my bank because they had to clear some stuff with them or similar. But after replying to that it's ready to go. Only it hasn't yet, sadly.
Whichever store you order from will likely require a credit card like VISA and it will be billed when or before they ship.
What the tax might be for computer games in Finland I have no idea, but you can probably find out by googling or looking at some government site. In Sweden it's 25%, I think. And that would be 25% of the ENTIRE sum, including shipping and any insurance.
Oh, and so far, I have not had any problems with anything that I have ordered, so I am a satisfied customer. Don't know specifically about EB Games, but they seem legit enough.