When you first decide to take that big leap and move your camera off of auto, exposure is the first thing you're really going to tackle learning.
In order to master exposure, you will need a working understanding of the exposure triangle and plenty of practice prioritizing and making decisions in the field.
The exposure triangle consists of the three main elements that make up a good exposure: aperture, shutter speed, and ISO.
Aperture- Think of aperture like the pupil of your eye, how open or closed the lens opening is determines how much light reaches your camera's sensor. It is measured in fractions, or f/stops. The larger the number, f/8 for example, the smaller the opening and the less light that reaches your sensor. Smaller numbers, like f/2, have wider openings and allow more light to reach your sensor.
Aperture also has an effect on depth of field, the area in front of and behind the focal point that is sharp. A smaller number will result in a more shallow depth of field, leaving less of the image in focus while a larger number will result in a deeper depth-of-field, leaving more of the image in focus.
Shutter Speed- This is the duration of time the shutter remains open, therefore the amount of time the sensor is exposed to light.
Lower shutter speeds create motion blur and higher shutter speeds freeze action.
Shutter speed is the most important factor. If your shutter speed isn't high enough to render a sharp image, and if that wasn't an intentional creative decision, you may as well have missed the shot. Even with Photoshop, there really isn't much hope of saving a blurry image.
ISO- ISO is a pretty simple concept. It represents your camera sensor's sensitivity to light. The higher the number, the more sensitive your sensor is.
Creatively speaking though, higher ISO's introduce noise into your image. Personally, I go all hipster artist when my images have too much noise...it works, but it's definitely a creative decision I have to make, oftentimes on the spot.
If my vision of the final images is high contrast and sharp, a high ISO is not going to get me there. If I'm documenting an event and there isn't a lot of light and I cannot, for whatever reason, use flash, I will likely choose a little noise over underexposure.