You can make HDR photo from one single jpg shot made with your cheap compact camera! The better way to make HDR photo with a compact camera is to take at least 3 photos with different exposure: one underexposed using manual exposure correction (-2), one normally exposed and one overexposed (+2). But you can make pseudo HDR photo from one single jpeg in Photomatix. You even don’t need to make underexposed and overexposed versions of this single photo in Photoshop.

1. Just open twice the same photo in Photomatix (Ctrl+O).
2. Generate HDR photo (Ctrl+G); click Ok on the all popup windows leaving settings by default.
3. Apply Tone Mapping (Ctrl+T)

The Tone Mapping in Photomatix helps to get some details back. While there’s can’t be silver bullet settings and every photo needs individual approach you can start with the following:

Luminosity: between -2 and +2
Strength: between 40% and 70%
Saturation: between 30% and 60%
White Point: 1,7
Black Point: 0,010%
Smoothing: very high
You can play with tabs: Color, Micro, Saturation/Highlights as well.

Try to get not too much noise and saturation. Higher luminosity reduces halos, but creates a lot of noise. The lower you set the general Strength the less noise and halos you will get. The Photomatix manual which you can find in program directory perfectly explains every detail of its powerful settings.