How long did he pray?

By the time Alma the Younger was visited by an angel and called to repentance, he had become "a great hindrance to the prosperity of the church of God; stealing away the hearts of the people." (Mosiah 27:9)  There's no time frame given for how long he was out leading people into iniquity, but I imagine it was several years to have the kind of effect on the whole church as described.

When the angel finally appeared, he told Alma and his comrades that he was there because, "The Lord hat heard the prayers of his people, and also the prayers of his servant, Alma, who is thy father."  (Mosiah 27:14)  I imagine that Alma especially had been praying for his son since his birth, and really praying long and hard for many years.

Mosiah 27 teachers us that prayer is indeed powerful (Alma was awoken through fasting and prayer also--v 22), but that the answers to prayers are not necessarily timely, at least not to our reckoning.  It can get frustrating praying for people to have the kinds of experiences that, like Alma, will cause them to accept the redeeming and "marvelous light of God" (v 29).  This chapter gives me faith and patience, knowing that the Lord loves those that I pray for, and that He will "snatch" them out in His time (v 28).