If a team needs 1 run to win and the player hits a Six(6) then, How many runs would be considered? Would it be considered 1 run or 6 runs?
If the batsmen do not take a single run while the ball goes to the boundary line it will be considered a six and 6 runs will be added to the batsman's total runs as well.
However, there is an exception. If the bowler bowls a no ball, and the batsman hits a six off that ball, the six is not counted. Only an extra run of a no ball will be added in the team's total.
hims056's answer is completely correct, but just to quote the actual Laws on this one (Law 21.6(c)):
If a boundary is scored before the batsmen have completed sufficient runs to win the match, the whole of the boundary allowance shall be credited to the side’s total and, in the case of a hit by the bat, to the striker’s score.