Ok! We are on to it! :)

Welcome into the mazes of Italian bureaucracy! ;) 

Not at all, Shinji! :)

Maybe I've understood...

They are asking to your company (I guess it should be an Italian company), about your employment,
to declare... 
DI AVER ASSUNTO ... to have (just) employed...
DI AVERE ANCORA ALLE PROPRIE DIPENDENZE ... to still have as employee...
Il cittadino straniero <> nato a <> il <> di nazionalità <>
... the foreign citizen <you!> born in the city <> in the date <> with the <> nationality
dal <1> al <2> con la qualifica di <3> C.F. <> con retribuzione mensile di euro <>
from <1> to <2>...
<1> <2> duration of your contract for your company
<3> manager, executive, clerk, employee...

Contribution taxes, as I said, are taxes that companies pay on behalf of worker. Just for example if your gross monthly salary is 10.000 €, your company gives you 6.000 € and pays 4.000 € taxes on behalf of you. At the end of the year you will pay the difference if you ought more, or will get money back if ought less.

1.
"residente a" where you are living at the moment "cittadino/a" your citizenship

2. (probably they are asking to your company)
DI AVER ASSUNTO ... to have (just) employed
DI AVERE ANCORA ALLE PROPRIE DIPENDENZE ... to still have as employee
 
3.
Il cittadino straniero name and surname nato a birth place il birth date di nazionalità nationality 
(I guess here something is missing)
dal from date al to date con la qualifica di qualification C.F. Italian fiscal code con retribuzione mensile di euro monthly salary 

4. 
Di aver assoloto gli obblighi in materia di contribuzione [Si] [No]
... to have paid contribution taxes (taxes that companies pay on behalf of worker) and made documents about it

hahaha, yes, I'm struggling. Italian post office, prefettura, comune, immigrazione... I'm in the mazes!

Thank you for your help!!

Yes, I have to ask my company to fill in on this document, but my company is a Japanese comapny, they don't understand the meaning of this document, so I have to translate it.

I've been employed in my company since 2010 as a employee, so

DI AVERE ANCORA ALLE PROPRIE DIPENDENZE ... yes

dal 2010

al I will fill in nothing 

con la qualifica di dipendente

Di aver assoloto gli obblighi in materia di contribuzione [yes?]

my income tax, social insurance premium, etc, are decucted from my salary, so I think yes

Thank you very much! Grazie mille!