Ok, so this is a very general method and I'm sure you can find a lot of videos of it if you need more info (key words: analyze particles imagej, counting cells imagej, countine nuclei imagej).
Usually to analyze nuclei you would use the analyze particle tool after thresholding the image. However, the threshold is not very good with this much background. The rolling ball background subtraction tool in imagej handles this very well, and improves the thresholding giving you a more sensitive segmentation of nuclei (it doesn't only register the very bright ones).
Process >> Subtract Background... >> Play around with the settings, I used a ball radius of 100 px, it worked fine. See the wiki for more info on the settings.
On the subtracted image: Image >> Adjust >> Threshold >> Manually adjust threshold untill you have a satisfactory mask.
On the thresholded image: Analyze particles >> Again, experiment with settings, the most important for you is the size of the smallest and largest objects you want to detect, I used 50-500 I think. And circularity 0-1. >> Check the add to manager box.
Your cell number is the number of ROIs added to the manager. I assume you don't care about measuring intensities in the nuclei, so I won't elaborate on how to do this. But you can figure it out with the help of google if you need it!
PS. If you want to create an overlay of the ROIs to the original image, like the one I posted:
Image >> Overlay >> From ROI manager