You have not shown where the power is coming into this diagram, there
should be black and white wires leading back to the panel somewhere in there. It doesnt really matter for just tying into the existing light circuit, but if you wanted another switch it might be more relevant.
Basically the hot wire (black) will bring power from the breaker to a switch, and from there it goes to the load and makes a complete circuit back to the breaker panel on the neutral (white) wire. An outlet is always energized (unless it is a switched outlet, which could be possible if this wiring was done a long time ago). A dedicated outlet will have wires routed back to a breaker as well. These days code would have them on separate circuits, I think, and that outlet would have to be GFCI if it was in a bathroom (this is a cheap and easy upgrade by just putting in a new GFCI receptacle, and it would be a good idea to do that while you are in there). Dropping a hair
dryer into the tub used to be fatal, but for 30 bucks it doesnt have to be.
So; If you want to put the fan into the light circuit, then you would just splice it into the light fixture wiring. Inside the fixture there should be two wire nuts, one with the black wires, one with the white. Just splice in the wires that lead to your fan; black with black and white with white, and it will turn on when the
lights go on. There should also be a green or bare copper wire in there that is the ground. Connect that as well. If there is no ground, I would suggest you get an electrician to update your house's wiring, as it needs it.