Using the built in camera app, Sight 360, and ProShot (which I personally recommend). Pictures are not very good as the camera is not very good on this phone, but they aren't blurry.
Autofocus is slow and inaccurate for some shots with this phone. I think a lot of it has to do with poor choice of exposure values sometimes being used in auto, especially when combined with more complex scenes in terms of subject and light.
In Camera App - go into settings and force a -2.0ev. That helps exposure and, IMHO, focus time/accuracy
If the pic is going to be out of focus you should see it on the screen - disabling tap the screen to take a picture allows you to tap the area of the screen you want to focus in on and that engages manual focus
Like Philip, I advise using alternate Camera Apps - he likes ProShot which is feature rich in terms of manual and saved settings, I prefer Camera360 Sight for point and shoot ease - either is a huge improvement over the stock Camera App
I find low-light photos are extremely blurry and grainy. Daylight photos look pretty good. I'm using ProShot. The default Camera app doesn't focus properly. As a result, all my videos go in and out of focus even when the subject is static.
The most common correction for grainy low light photos is to decrease ISO.
ProShot has 2 customizable "slots" that will save settings for you. On my ProShot I have the C1 (Custom 1) saved with ISO 100 and that is the one I'd select for low light, no flash.