How I can manage to take HDR or bracketed pictures with the Nikon J1?

I have been fiddling with the settings of this camera but it seems hard for me to figure out how to take shots with different exposures. Either I'm not getting the ISO, shutter speed etc.right or I just don't know how this camera works.

I'd say it's a combination of your lack of knowledge and a lack of skill. I'd also suggest you do some serious reading about exposure, shutter speed, aperture and light - learn the relationship between these four, read your owner's manual cover to cover because it's apparent you've not done that either.

I searched your manual for both "bracket" and "HDR" and could find neither. I derive from this that the J1 doesn't do bracketing. I'm more than a little surprised. This is the manual that I searched.
http://www.nikonusa.com/...1RM_EN.pdf

Andy,

Your camera doesn't provide AEB (auto exposure bracketing) - which would be the easiest way to capture images for HDR (high dynamic range imaging).

So that leaves you the option of taking 3 (or more) shots with settings that you fix. The minimum number would be 3 (one underexposed, one normal, one overexposed).

You'll have to have your camera on a tripod, of course, so that it doesn't move at all from one shot to the next.

The following settings should stay fixed:
White balance
ISO sensitivity (highly recommended)
Aperture
Focus

Just change your shutter speed (anywhere from 1-2 exposure values per shot - keep the spread consistent no matter what you decide on for all 3+ shots).

Google "HDR" or get a library book to figure out the best ways to produce such images (R.C. Concepcion of Kelby Training has a good book on the topic). The initial look of super fake surreal overly grungy HDR images is really past its prime. People got that nonsense out of their systems already. Nowadays the trend is to use HDR in a more realistic-looking way.

Good luck. That camera isn't one of the best. It's missing some key features and has a skimpy processor size. But you can probably still eke out some images that you will enjoy… Happy shooting.