HDR on Nikon D3200, exposure problems?

Every time I alter the aperture on aperture priority, the shutter speed adjusts itself automatically but I don't want that, because I want to take some under exposed and some over exposed, but it adjusts itself so that the photo just comes out the same? If that makes sense.

It's because you are shooting in a semi-Auto mode - the camera thinks you want the 'correct' exposure

You shouldn't be altering the aperture to do HDR in any case - as it will affect the depth of field in your series, you need to be altering the shutter speed!

This is how you do it;
- either shoot in manual & ONLY adjust the shutter speed by a third/half/full stop each time to under or over expose (look at your light meter in camera & adjust shutter speed until it's either + or -).
- or if you are not comfortable shooting in manual, shoot in aperture priority mode (A), and adjust the EV comp button (+ or -) between each shot - this forces the camera to under or over expose.

Make sure Auto ISO is turned OFF.

This tutorial may help

http://aviewfinderdarkly.com.au/2013/07/05/how-to-take-hdr-photos/

To do what you want, the simplest way is to set the camera to Auto Bracketing which you can find in the menu (I'm assuming your camera has that facility)
In this mode, you can take three photos and the first will be normal exposure; the second will be under exposed and the third one over exposed.
You can usually set the amount of exposure adjustment in half stop increments.

I'm a Canon man so, sorry, I can't tell you much more about your Nikon but I'm sure you'll be able to do that with your camera.