[FEN "8/8/8/8/3k1KB1/8/8/8 w - - 0 1"]
I am new to chess and have no clue as to how to win this game. Which moves can be done with what is on the board in order to win? Could anyone explain?
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This position is a draw, the game is over. It is not possible for either side to checkmate the other from this position, not even if the side with the bare king would try to help.
The same is true for king and knight vs king. A single knight or bishop without any pawns or other pieces is not enough to win the game.
With king and two knights vs king it is in theory possible to checkmate the other side, but it can't be forced. It's very easy to prevent the checkmate as the defending side. So that is essentially a draw too.
It's a better idea to always keep a pawn or two on the board so you can promote one.
If you look closely, the bishop only attacks on squares of a specific color (in this case, it's a light square bishop). As long as the opponent king steps on dark squares, it's impossible to 'check'mate the opponent king. During the endgame with very few pawns on the board, it is most likely best to sacrifice your piece for an opponent's pawn, as they have very big potential of promoting. As said before by @RemcoGerlich, it's a good idea to keep more pawns on the board so you have more potential.
As an example, if you have King + Pawn vs King + Bishop + Pawn, there's no point trying to exchange the pawns, as that would lead to a draw. You can instead take away your opponent's pawn with the bishop, leaving a King vs King + Pawn which hopefully would not lead to a draw.
Generally, when asking how to win a game, you will ask for a particular player. For example, you can ask: How can White win this game? In fact, that seems to be what you are really asking here.
However, this position is a dead position: neither player can achieve checkmate through legal moves, no matter how badly the other player plays. Under FIDE (World Chess Federation) rules, this automatically causes the game to end in a draw . As soon as a player or an arbiter notices this, they should stop the game.
Of course, casual players are free to ignore the previous paragraph. What happens if we try to achieve checkmate in this position? We might get something like:
[FEN "8/8/8/8/8/5B2/8/5K1k w - - 0 1"]
The Black king is in a corner (h1), with only three adjacent squares. One (g2) is controlled by the bishop and one (g1) is controlled by the White king. It can still escape to the other square (h2). We can't do any better than this, so we can never get checkmate.
There are some variations that would allow checkmate. Some have been covered in other answers. One very interesting one that has not been covered is to give Black a pawn. This can actually hurt Black!
[FEN "8/8/8/8/8/5B2/7p/5K1k w - - 0 1"]
To get this position using legal moves, first move the pawn to h3 and the bishop somewhere off the main diagonal. Then move the kings into position. Finally, move the Black pawn to h2, then move the bishop onto the main diagonal, giving checkmate!
 Assuming the preceding move was legal and complied with the touch-move rule.