The word 'about' does not have a direct translation. The nearest would be 'Leggono su giornali.' - They read up on newspapers - They studied about newspapers.
My comment above: 'Leggono dei alcuni giornali' should be 'They read some other newspapers.'
We see lots of people trying to make 'word for word' translations, and often it just doesn't work.
Here's some info about it from about.com: http://italian.about.com/library/fare/blfare125a.htm
I am using a grammar book published by Wiley and it includes a section about "di + definite article" meaning some/a few. I think it is included in this section because often that combination is possessive, but it is teaching that there is another meaning for it as well.