Well this is a subject and a half and one I could talk about for a long time so I am just going to scratch the surface with it and let you all experiment from there.
Photography is like cooking in an oven. Cooking is all about getting the correct amount of heat to whatever you are trying to cook. Photography is all about getting the correct amount of light to 'light' your subject. The three things that are going to make a difference to your meal coming out burnt or not are 1 - the temperature, 2 - the time its left in the oven and 3 - how high up it is in the oven as heat rises. So understanding all that in photography terms I would liken Shutter speed to be the time it in the oven, aperture to be how hot the over is and ISO to be how close it is to the top of the oven. In the same way as cooking these 3 things control the exposure of a image. So still going with the cooking analogy if you put something to the top of the cooker at the same heat as it was at the bottom it is going to cook quicker if you do not turn down the temperature to compensate. if you do not compensate you meal will burn. Same with photography, if you turn up the ISO but don't tweak the shutter and/or the aperture then your image will be overexposed and the camera makes one or all of these for you when you shoot in any mode apart from manual or bulb.
But what happens if you like you meal a little overdone? Or maybe even rare? That is where manual mode can help as the camera's programmers don't always know what you want. It is also worth mentioning on a lot of modern DSLRs nowadays there is a little line with an indicator the that runs through the bottom of the view finder, consider this the cooking instructions advising you that you are getting closer to the settings it thinks you should use, if the indicator is in the middle of the slider, you would be following the recipe to the letter - correctly exposing according to the programmers of your particular brand of camera. If its towards the left that indicates the image would be the amount under exposed and the right is going into over exposed. Again to change exposure you would have to tweak the ISO, Shutter Speed and/or the aperture understand this concept you will be well on your way to going manual on any camera. There is a lot more to gaining more control of pictures than this brief introduction but this should give you an idea of how to start exposing your pictures manually.
Please leave any comments below. Happy Shooting.