1) 10% Standard DeductionThis may be a misleading name but it is a way to pay less tax anyway. During the first 2 years you live in Norway, you may be entitled, as a foreigner, to a so-called "10% Standard Deduction". This does not mean you pay 10% less taxes but that the gross income you are taxed on is reduced by 10% (you have to pay tax on a lesser income, therefore paying less tax).
This is not done automatically and you have to claim it. When you get your tax paper (with your income, how much tax you have to pay, whether you paid too much or too little tax, etc...), you have the possibility to either accept it (and not do anything) or ask for some corrections. If you want to pay less tax, use the second option. Enter in the corresponding paragraph (ask for help if you have some doubt) that you are a foreigner who has lived in Norway for less than 2 years and the tax to be paid will be recalculated.
For more information: http://www.skatteetaten.no/en/International-pages/Felles-innhold-benyttes-i-flere-malgrupper/Articles/10-Standard-Deduction---Income-Year-2008/
2) BOLIGSPARING FOR UNGDOM (BSU)
The name may seem mysterious to you if you don't speak Norwegian but it is actually quite straight-forward. It means to save money ("sparing") to get a property ("bolig"). But what is that and what does this have to do with tax?
This is a bank account you should get if you are 33 year old or less. It is basically a way for Norway to motivate young people to spare money for a future property. When people are 25 for example, they don't imagine how expensive properties are and may not even think of getting one. To help them think about it, the authorities have decided to reduce taxes to people having a BSU account in a bank.
What you need to do? Go to your bank and ask for some more information. They know for sure what a BSU is and it will probably not be any problem for them to open a BSU account for you. What will it change? You will be able to pay less tax. The more money you put in this account the less tax you will pay. The limit is 20 000 NOK per year and it is recommended to reach this limit every year (best return on investment).
These were the 2 things I knew of to reduce tax, and I was lucky to have people tell me about them when I arrived here, so I thought I had to share them on the internet for everyone to benefit from them.