If you have a cheap compact camera but want to make HDR pictures like these it is the right tutorial for you.
You will need a software called Photomatix Pro. I have downloaded mine from here: http://downloads.tomsguide.com/Photomatix-Light,0313-32925.html
It is free to use but without the license key you will have a watermar on your picture. But google is your friend... :)
First things first you need to make 5 pictures with 5 different exposures. This is not easy because with a cheap camera you have to set the exposure manually aftre each picture meanwhile you hold the camera perfectly still. I advise to put it down somewhere. The five exposure setting are -2, -1, 0, +1, +2. The pictures will look like this.
After this you open up Photomatix Pro, selet all 5 pictures and drag them on Photomatix.
Select "Merge for HDR processing" and hit enter. The next window you can leave the default settings.
The next screen on the right side you will have some presets and on the left side some settings to play with.
For this image i have used the "Creative" preset and set the saturation slider to maximum.
When you like your picture hit "Apply" and after that "Save Final Image" and choose jpeg.
And that's it!
Here is the final image.
Have fun making your own HDR images.