We almost always use the postal system (USPS) to send packages. You can get cost estimates using the international shipping calculator at USPS.com and here are the full price tables and restrictions on shipping to Norway:
http://pe.usps.com/text/Imm/mo_029.htm#ep1747220
Alternatively, you can just go to the post office, where they can weigh the package and then tell you about the different options.
The US post has stopped offering surface mail (very cheap, but very slow) for international shipments, so standard air mail is now the cheapest (and slowest) option. Unfortunately, you can only use it for small packages (under 4 lbs). Also, this method of shipping does not usually have tracking options.
For larger packages, the next cheapest option is International Priority Mail. For shipments over 5 lbs, you may be able to benefit from the $39 Flat Rate shipping boxes if your contents will fit. There's also a larger $50 Flat Rate box that will save money on shipments over 9 lbs. For regular shipments (not in Flat-Rate boxes), the price is scaled by weight.
For slightly faster shipments, you can use International Express Mail, but when shipping to Norway, I haven't noticed that it's significantly faster.
The easiest way to actually send things is to just take the shipment to the post office. You can sometimes save a little time and money by paying for the postage online, but you will probably still need to take it to the post office to drop it off and fill out the customs form. On the customs declaration, you'll need to give a brief description of the contents and their value. (If, based on that information, any import duties are owed, the recipient is usually responsible for paying them when the package is picked up.)
If you need something sent extremely quickly (within a few days), you'll probably need to use a private shipping company. You can get cost estimates on their websites, but FedEx and DHL are likely to be your best options. UPS tends to be quite a bit more expensive when shipping to Norway. In this case, you'll probably need to go to the company's offices or affiliated stores (i.e. Kinko's, Mailboxes Etc, and others) to drop off and pay for the shipment. You'll also need to fill out a similar customs declaration form.