DOF vs Shutter speed

I am confused. If I am in a wedding or party. I want a low aperture setting (ex: f1.0-f2.8 ). Large aperture give you more light BUT also give you shollower DOF. Shollow DOF will Blur image very easily with your subject moving around. How can you take a sharp picture of moving subject with shollow DOF?
1) I can change the aperture to F4 or F5.6 to give it large/deeper DOF.
2) I can use f1.8 with higher shutter speed to freeze action. doing this will darken the picture. than i have to use flash to compensate. what if location does not allow flash?

But that just beats the purpose of having a f1.8 lens. So is shooting with large aperture hit & miss to get a sharp picture? correct me? what am i missing. I am sure something simple i am not understanding.

I don't think "hit or miss" is the right way to think about it, but using f/1.8 (especially when you're in tight on the subject) definitely requires practice and skill.

Ultra Sonic Motor

If your lens autofocuses fast, you will be able to get the shot. Also shoot a lot. The more photos you take, the higher chance you will have some in focus =)

Also I think you are mistaken, smaller f number = larger aperture. A lens set to f1.8 is gonna let in 8 times the light a lens at f5 is gonna let in. If you set your lens at f1.8 you can afford 8 times faster shutter than at f5 (just comparing the 1 to 2) So if you are taking at 1/200 at f5, you can take at 1/1600 at f1.8. If you need a flash at f1.8, you WILL need a flash at f5 also =)

when you have shallow depth of field you just have to choose where the focus is better. Its not that the entire picture is blurred, but that the amount of picture in focus is less. Put the focus on the face/eyes and the picture will be great.

1. practice taking pictures of moving subjects
2. raise ISO

This one reason why fast lenses will never replace good lighting - you have no DoF control with moving subjects.

If the subject is moving, use AI servo instead of one shot. The camera will continually refocus as your subject moves.

To address point #2, there should be no reason that the picture darkens other than your purposely pushing the shutter speeds so high that your exposure is no longer correct. If you want to maximize shutter speeds to freeze subject motion, shoot wide open as you are and raise the ISO until you get the shutter speed your looking for.

For instance lets say a properly exposed picture at f/1.8 is ISO 100 at a shutter speed of 1/50. By raising the ISO to ISO 400 your settings would be f/1.8, ISO400 at 1/200 and the exposure between the two pictures should be identical.

Not sure if I follow your question correctly but if you are getting underexposed pictures shooting wide open with the 50mm 1.8 and can't use a flash, you can always bump up your ISO.

Most lenses aren't the sharpest at their maximum appertures. Try shooting at 2.0 or higher with the 50mm and see if that helps.

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Make sure you've set your camera's autofocus to AI Servo. Then, half-press the shutter release button and let the camera track the moving subject. Use the Center Focus point only.

The ideal scenario is to use low iso, a dof that allows you to have everything (you want) in focus, and a fast enough shutter speed so you don't get motion blur. Sometimes light wont allow it so you have to compromise: use flash, bump your iso, lower your speed, or open your aperture.
At large apertures (f1.8) your dof is very small. If after raising your iso you still need to shoot wide open, get the key part in focus. If you are shooting people focus on their face, if you are close enough focus on their eyes. Check examples of portraits and you will see that most people use shallow dof and while their ears and the tip of their noses might not be in perfect focus, if their eyes are sharp you see it as a pleasing picture.
If at all possible use the shutter speed you need. Remember you can make a decent photo out of a noisy picture, but to correct motion blur is very hard.

Why do you think everyone gets excited about how the newer cameras can do decent ISO 6400. Sometimes it is the only solution!

Ideally you add light, if not, you compromise on DOFand ISO noise.

BTW if you need some more detailed info you can read "Understanding Exposure" by Bryan Peterson. Excellent, simple, complete reading.

1) Use AI servo for moving objects at all times! One shot is useless with movement and AI focus is just useless!
2) Up your ISO! It doesnt matter if there is noise in the image at higher ISO, its better than no image or a blurred image!
3) Flash is sometimes the only choice