Essentially, the Magic Wand selects areas of a color.
There you go, five words. Now a few more for clarification: If, for example, you click on a red part of the image, the tool will create a selection expanding outwards from that point of any red pixels next to it, continuing to do so until it hits a different color. The Tolerance slider in the toolbar determines how picky it is on how close the color has to be to the first pixel you clicked before it stops selecting.
Honestly, the easiest way to see what it does is to play with it - draw a black Filled Shape on the white background of a new image, switch to the Magic Wand, and click inside and outside the shape. The tool expands out until it hits the boundary between the colors, essentially selecting the shape or everything outside the shape.
As for Smudge, it is not built in to Paint.NET, but you can install a plugin that allows you to smudge a layer.
You can find out more about the plugin here:
In the future, try giving http://searchpaint.net a shot. Searching "Smudge" returns the plugin you need as the first result.
Regarding Cropping, there is no dedicated cropping tool, but there is Crop To Selection. The command does exactly what it says: crops the image to the size of the active selection. When an active selection exists, the button on the toolbar becomes clickable. So, to crop a photo, use the Rectangle Select Tool to draw a rectangle around the part of the image you want to keep, then hit Image > Crop To Selection or the Crop To Selection button on the toolbar.