1. 75 ohms is a bit low, you may pull too much current....more than the IC can handle; you need to be, at a min, 220 ohms. 470 ohms would be better.
2. Based on your statement "when I press two buttons", you need to connect one side of each button to the 5V source, and the other side of the switch to each of the AND inputs. You will also need to add some pull down resistors to ground on those inputs. This will guarantee that the inputs are low/zero when the buttons are not pressed, and high/one when the button is pressed. Because this is a AND gate, both buttons must be pressed to get the output to go high. To turn on the LED under this conditon, the LED must be connected to the output (observe polarity!), and then through the resistor to ground.
However, you must realize that the LED will only illuminate when both buttons are pressed...release one (or both) and it will go out...it will NOT remain lit.
This begs the question...why are you thinking of using an XOR? You don't need it to obtain the above effect.
Charlie