Probably the best place to start is a google search for this surname. Include terms like family, family tree, or genealogy.
Go to the major genealogy sites and search for the surname. Some of these sites are subscription sites, some are free. Some of the subscription sites may be available at your public library; some are available for use at an LDS Family History Center.
Get a Family Search account, it is free.
Keep in mind that the quality of internet genealogies is quite variable, regardless of what site they are on. You will need to validate what you find.
There are a number of good books on genealogical research, and specifically on using the internet. You can find these in most bookstores, as well as your public library.
With some luck, you will end up looking at Norwegian records. You don’t need to be fluent in Norwegian, but knowing certain key words is essential. A number of sites will have lists of Norwegian genealogical terms.
There are presently only four Thodesons on WikiTree, so if you end up putting your information here, you will covering new ground.
Best of luck.