How to check for sensor dust

Assuming your camera allows some sort of manual control:

1. Use a narrow aperture e.g. f/22
2. Shoot a light even background e.g. blue sky or white sheet of paper
3. May need to, say, +1 EV if shooting white sheet of paper to ensure proper exposure 
4. Manually set the camera out of focus
5. Slightly shake the camera while exposure in progress, usually a few seconds
6. Examine using camera LCD, magnifying the image to see the dust

Alternatively you can also load the image into software like Adobe Lightroom and examine from there.  Lightroom 5 has a feature called Visualize Spots which is very handy to identify sensor dust, and subsequently clone them out.