As far as I know knowledge of Latin was a pre-requisite for obtaining roman citizenship or holding public office, although If I remember correctly that became more lax in late antiquity.

In the late republic and early empire timeframe "latinization" happened mainly through legionaries that had completed their service, they were given territories in newly conquered lands to farm and would have naturally introduced their language and customs, also in many situations legionary forts attracted a great deal of people around them, where there are idle legionaries there is business to be made, a legionary would have needed things outside of what the military could have given him and had money to spend, many towns started out like this (like Colchester in Britain, formerly Camulundum), frequent contact with soldiers would have spread knowledge of latin.

I think the major factor would have been simply the vast amount of influence the romans projected in and outside their territories, simply the possibility of dealing and trading with the romans was enough of an incentive to learn the language, of course a peasant in some far off province might have never learned latin but a merchant or anyone that held public offices would have likely known.

I remember an account of the Eastern roman diplomat Priscus about his travels in Hun territory and at Attila's court, how he mentioned that the Huns spoke latin because of their dealings with the (western) Romans.