I'm really struggling with the sharpness of my pictures. I use a Nikon D3100 with prime lens 35mm f/1.8. Every time I take a picture, doesn't matter outside or inside, they all come out not sharp enough. What am I doing wrong? Also, if I'm trying to photograph kids that move all the time, I need the camera to focus really fast, but seems like with these lenses you always have to focus yourself by rotating until it's sharp enough and sometimes it doesn't even come out sharp enough. How can auto focus quickly so the pictures come out really sharp?
Can you get a very sharp image with careful manual focusing?
To start with, I'd test the components to make sure all is working properly. Put the camera on single point focus, AFS, center the focus point, and aim at a stationary object with a fairly high shutter speed or a tripod so that camera shake is not a factor. If you cannot get sharp focus then, I would suspect a problem with equipment. Remember that depth of field at f/1.8 will be very shallow, though. If you need more depth of field, try to keep it around f/8. At apertures smaller than about f/11, diffraction may begin to decrease sharpness, so don't overdo it.
Try it at different distances, brightnesses, F stops and shutter speeds, and see if it makes a difference.
You might try using the same settings and live view too. Live view uses a completely different focusing system. It's slower, but because it actually senses focus on the image plane rather than using an AF module, it can be very accurate. If pictures using Live View are significantly sharper than those with viewfinder AF, then your camera's AF may be out of adjustment and need service.
My D3200 with a much slower kit lens focuses at a pretty decent rate, when using AFA and dynamic-area focusing. When it hits, it's good and sharp. A f/1.8 lens should do better. However, it's a gamble with multi-point AF, as the camera does not always guess right what the subject is, so do not use that if you have a chosen subject on which to focus. It also helps if you're following moving action, to prefocus at a distance near where you expect the action to take place. The closer your starting point is to the final focus point, the faster your AF will get there. There's some guesswork there, but predicting can help.