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.
I'm not an expert but I compiled the following to better understand and explain. In this sentence, dei (or de + i) is a partitive article or articolo partitivo in Italian. IT MEANS "SOME". Below is an explanation if you are interested.
Definite articles: il/i, la/le, lo & l'/gli as in Voglio i libri = I want the books (specific "the")
Indefinite articles: Un, Una, Un', Uno For example I want a book = Vogio un libri (any book); Un'arancia = an orange; Uno psicologo = a psychologist (z, ps, pn, x, y, gn or s + consonant)
There’s no plural, indefinite article in Italian so they use
a) adjectives like qualche, alcune/alcuni as in alcuni libri = some books
b) pronouns like alcune/alcuni, ne, certe/certi as in certi libri = certain books
c) adverb un po' as in Dai un po' di mele = Give some apples
partitive article or articolo partitivi which is, yes, di + article to denote "some" Del/dei as in Mangio del pane = I eat some bread or as in our case Leggono dei giornali = They read SOME newspapers
dell'& dello/degli as in Hai dello zucchero = Do you have some sugar
della, dell'/delle as in Ho visto delle ragazze = I saw some girls
The confusion comes from the preposition Di + article which (a) usually means "of" and the following:
(b) Originis as in "from": Io sono di Venezia or Di dove sei? = where are you from
(c) Topic as in "about": Molti italiani parlano di calcio = Many Italians talk about soccer.
(d) Comparison as in "than": I am bigger than her = Sono più grande di lei.
(e) Possessive as "'s": Caesar's crown = la corona di Cesare
(f) Materials as in made of: Wool sweater = Maglione di lana
(g) Time as "in" or "during": Working in the daytime = Lavorando di giorno.
(h) Movement as "by" or direction: Pass by here = Passa di qui; Go upstairs = Vai di sopra
(g) Some verbs are followed by "di" usually meaning "of", "by", "with", "about" as in Bisogno di = In need of; Innamorarsi di = to fall in love with; Non mi sono dimenticata di lei = I haven't forgotten about her
For 'uncountables', like salt or water, or whenever the amount is uncertain, we use 'some' or 'any' in English expressions as e.g. "Here, - have some water". It's called a partitive article and its Italian equivalent is formed using "di", of/from, and the definite article, il/i/la/le, - in this case "dei".
To instead say "of the" we would have to use da and the definite article instead, - dai giornali.
If you want to read up on this I think I can recommend using ThoughtCo