There was a time, signified by this day of Pentecost, when the church was unified—perhaps as unified as it ever was in its entire history. These verses reveal two elements of the time when the unity of the church was at its very peak.
1) They were devoted to the apostles' doctrine. In the first century, that was "the faith once delivered." It means they were constant. They were resolute. They were single-minded. They were determined in learning and following it. They did not drift. They did not swerve from it, and it produced what it is supposed to: faith in God; faith in His way; faith in His church; confidence and trust in putting these things into practice. They were deeply convicted.
2) They took care of each other. They were very much concerned for their brother's welfare. This was not communism, where they sold all their goods and turned them over to the administration of the church to distribute equally to all. But, rather, it indicates they voluntarily looked out for each other personally (individually), striving to meet the needs of each other.
This is the epitome of "feeding the flock"—and ALL of the body is participating, not just the ministry. Everybody is nurturing everybody else. The whole body participating in two major things, pursuing the faith once delivered and taking care of each other.
The New Testament epistles make it very clear that later, when the first century church was splitting, the people were counseled to get back to the faith once delivered—which means that they had drifted from it. They were no longer doing the things they were doing in Acts 2. Again, why? Why counsel them to get back to the apostles' doctrines?
Putting this together, asking where faith arises from, there are two major components. The first is God and what He does (I Corinthians 2). He opens up our mind. He predisposes it for us to receive something. The second is expounded upon by Paul in Romans 10. "Faith comes by hearing, and hearing comes by the word of God." Those two work together. What God does, by a miraculous act of His mind, of His will, of His Spirit working in our minds, is combined with the message He gives to the person He sends. It is to be the basis and foundation of our conversion and our faith. From that point on, it becomes a matter of learning more specifically the things that are contained within the message that was delivered to us.