Most likely the man’s relatives carried him to the gate each day. They would probably bring him in the morning before the first time of prayer and come to collect him in the early evening after the twilight sacrifices. The money which the man received from begging would then be used to contribute or help with his upkeep.1 Being crippled from birth means that the man spent most of his life as a beggar.
2 And a man lame from birth was being carried, whom they laid daily at the gate of the temple that is called the Beautiful Gate to ask alms of those entering the temple.