This is kind of difficult for me to answer in terms of the inhabitant of the contado. The answer to this question would have to do with how much business the individual did with within the city.
As far as the city dweller goes, Frederick Najemy estimates that 60% of the inhabitants of Florence had a degree of working literacy. That means an individual would read books of account, perhaps work out the meaning of the very basic Latin of rather simple notarial contracts, and perhaps read and write a letter if they had business interests further afield. This question is, however, hard to answer.
Notaries were important catalysts for the spread of the legal institutions fundamental for the expansion of medieval Italian commercial interests. As the proliferation of commercial agreements took off (commenda "type" contracts, apprenticeship contracts, etc.), the desire to understand these would have also increased.
That said, the increase of the presence of notaries should not be seen as having a direct relationship with literacy levels. Benjamin Kedar has noted that Genoa had a rather small noatriate. This is strange since prior to the Black Death, huge numbers of Genoese were participating in trade through investment. This number was so great that there was not merchants guild as there were so many individuals who participated in commerce, thus giving rise to the stereotype ianuensis ergo mercator (Genoese therefore merchant). Kedar surmises that perhaps this is suggestive that the city had a high degree of literacy and thus the citizens did not need so many notaries to read and understand contracts on their behalf.
Hope this helps.
The answer depends on what you mean by "his own language".
In the case of the city of Rome, most of its inhabitants actually spoke the Roman dialect, in the form that most scholars identify as romano di prima fase (the variety in use between the 12th and early 16th centuries AD circa).
Now, except for a few documents that have been written by either friars or local notaries - such as the Diaries of Stefano Infessura, or part of the registry of the Confraternita dell'Annunziata - there's no proof whatsoever that your average peasant or citizen would actually write something down in his native dialect; the (rather few) examples we have are all the work of what we'd consider "learned" people. This is true as far as the Middle Ages are concerned.
However, things were going to improve after the mid-16th century, when poems (Giuseppe Berneri's "Meo Patacca") or plays (Cristoforo Castelletti's "Stravaganze d'Amore") written in that dialect - or at the very least in a somewhat diluted form of it, a heavily Tuscanised version of Roman - started being published so as to be performed in public.
As a last tidbit of info, keep in mind that people in the Papal States/Latium kept making use of the services of professional letter-writers (and readers...) well into the 1920s; I would therefore argue that most Middle-Age Romans were actually unable to read or write in either Latin or their very own dialect not least because of the rather shaky situation in (the already depressed, not to mention sparsely populated) town during that time - having to face such pleasant things such as the absence of the Pope, popular uprisings, wars, blood feuds among the nobles, etc.