The Viking Age is usually defined as spanning the 8th to 11th centuries. The core areas of the Vikings were Norway, Sweden and Denmark, but settlements has also been found various places in great Britain and Ireland, the Faroe Islands, Iceland and Greenland. When searching for sources to recreate Viking clothing, this is the "definition" I am using.
The clothing in Finland during this period seems to significantly differ from the Scandinavian dress tradition. For example, oval shoulder brooches doesn't appear until the end of the 11th century, and the characteristic "tortoise brooch" used by the Vikings is not found in Finnish graves. Also small bronze spirals are used to decorate aprons and mantles in a manner unique for Finland, a tradition possibly inspired by Latvia where similar kind of decorations is found. Because there are basic differences in dress tradition I usually exclude Finnish finds from the traditional Viking clothing.
The answer to what we know about viking clothing can be summed up in two words; "damn little". The only way to know what at least one Viking woman or man wore would be to find an entire set of clothing. And even then, we wouldn't know how the "average Viking" dressed, because there is no such thing. The Viking age spanned more than 300 years and a large geographical area, and it is reasonable to assume that just like in later periods, clothing varied according to time, geography and personal taste.
In addition, the clothing found in graves does not necessarily tell us what people wore in their daily life. Just like we don't usually bury our dead in T-shirts and jeans, the Vikings would probably not dress the body in work-clothes, unless that was all the person owned.
To make things even more challenging, with the exception of a few more or less intact garments, Viking clothing comes to us as fragments. This means that we have details about the fabrics that were used, including which materials they were made of, the patterns of the weaves, and the layering of inner garments and outer garments, but we don't know how most of the garments looked. Interpretations are made by different researchers based on the archaeological finds, Viking art and descriptions of clothing in contemporary stories and poems but this is still "best guesses" based on the scant evidence we have.
It takes me a long time to research and write these, so don't expect the list to grow quickly. The articles are built on what I know at a given point in time, and will be updated if I find new sources or new interpretations.
This is for the textile nerds (Yep, I'm one of them :-)
Books and article collections
Articles on specific textile finds