Prepare for walls of text
I'm not sure how many people actually know what the sliders they push around actually mean, so I'll just attempt to explain them here. I learn most of my Lightroom stuff from here so if you watch the videos there, you should pretty much know all this
So in this guide I will explain most of the stuff in the develop module, which is basically the same thing as Adobe Camera RAW (ACR) that is in Photoshop. I'll also put the shortcut keys in brackets (these shortcut keys work in Lightroom, I'm not sure if they work in ACR, but what they do is essentially the same)
Crop Overlay (R)
Simple, crop tool. You can choose the aspect ratio, so if you want a square crop, or you want to crop to print, use this. (actually if you just want to crop for print I recommend cropping it in the Print Module in Lightroom so you can still have the original photo for web purposes etc)
You can also adjust the angle to rotate the picture. I recommend using the ruler (click the icon beside the word "Angle") and just draw a line across a line in your image that is supposed to be horizontal, and then you're done correcting the angle
Spot Removal (Q)
Like a clone stamp tool, except you don't alt+click to sample, you click the area you want to "correct" and drag your mouse to the area you want to sample. You can change the area you sample from by clicking on the circles and dragging them around, and the size of the area you select by clicking on the edge of the circle and dragging it inwards/outwards, even after you let go of your mouse. If you just click on the spot you want to remove, Lightroom automatically samples an area close to the spot.
Size: size of brush, don't bother using the slider, just use the square brackets [ and ] to change the size. If your mouse has a scroll wheel, you can also just scroll it to change the size.
Opacity: I don't really touch that, if you want to remove a spot you'll want the opacity to be at 100% anyway
Clone/Heal: pretty self-explanatory, Clone, well, clones like the clone stamp tool, heal just works like the healing brush
Red Eye Correction
I don't think I need to explain this
Graduated Filter (M)
Adds a graduated filter to your image. Click and drag to add the filter. Where you start your first click will determine where the gradient of the filter starts. Holding shift while doing this makes the filter completely horizontal, if you want that.
Mask: New | Edit
Basically, you can add multiple graduated filters to an image. Clicking new gets you out of the existing graduated filter so you can add a new one.
Effect: Setting it to "exposure" or "brightness" or whatever resets all the other settings to the default, only leaving the setting that you selected unchanged. There are also presets available, and you can also save your settings as a preset.
I don't think I need to explain what the sliders mean, they are pretty self-explanatory. I will explain what Clarity does when I talk about the Clarity slider.
Colour: Adds colour to the graduated filter. If you want to add a tint to the skies or something, you can use this. The saturation slider will determine how much of this tint can be seen. When you up the saturation of the graduated filter, you are saturating the colours in that area where you added the filter. This will make the effects of the tint less noticeable. Go to 0 saturation, however, and the colour of the whole area will be tinted with the colour you chose. If you click in the colour selection panel and drag your cursor outside the box, your cursor becomes an eyedropper tool, where you can sample a colour from your image.
Adjustment Brush (K)
Everything is the same as the graduated filter, except this is a brush. Your presets will be more useful here than in the graduated filter menu, so for example you want to sharpen and saturate only the eyes of the model or something, just select a sharpness value and a saturation value and save it as a preset. The existing presets are pretty useful, like Iris Enhance, Soften Skin and Teeth Whitening. Use your creativity to come up with your own presets.
Brush: A | B | Erase
A and B are just presets for the size, feather, flow etc. I use Erase if I want to add a custom vignette, for example, when my subject is not to the middle of the frame and I want to add a vignette, I will paint over the whole picture with negative exposure (I will also up the saturation so the dark parts won't look so flat), then erase over my subject.
Feather: high value means soft brush, low value means "hard" brush
Flow: No idea what it does
Auto Mask: does what it says. Ensures you don't accidentally paint over stuff you don't want to.
Density: No idea what it does
Pressing O when in the adjustment brush mode shows you an overlay of which parts of the image are selected. Red = selected.
Some other useful shortcut keys or stuff
Y: Puts your before and after shots side by side for you to compare
Shift+Y: Cuts your photo in half, showing the before on the left, and the after on the right. Not very useful IMO, but you might find it useful
Backslash (\): Toggles between the before and after shots
G: Grid mode. Takes you back to the Library Module when you need it
D: Develop Module
L: Lights out. Press once to dim the lights, press twice to show your picture on black.
Tab: Closes both side panels
F6: Closes filmstrip (the bottom panel)
If you're in the lightroom develop module, you can see a little icon thingy at the left of the words of each panel (or if you're in the spot removal tool or graduated filter or whatever, you'll see the same icon beside the reset button. That one toggles the effects on and off, so you can see, say, before and after you add a graduated filter.
Double clicking on a setting (e.g. exposure) brings that setting back to the default, unchanged value.