Inkscape creates *.svg files, "scalable vector graphics." It's comparable to CorelDraw and Illustrator, and can save *.eps files which I'm told opens in CorelDraw (I've never used either).
Step 1: Import and Trace Bitmap
Then, when the image is selected, go to Path > Trace Bitmap. This takes the image you imported and generates paths that we'll be working with. For posterizing a picture, Color Quantization OR Multiple Scans in color generally works, but play around to find what you're looking for. Guestimate how many colors/scans will be needed (the more scans, the more detail and closer the path is to the image).
After clicking OK, the paths will be generated right ontop of the image. Using the selector tool, drag the paths away from the image.
Lastly, rightclick > Ungroup. The path is generated as a group of objects; each color is represented by a different object, and the objects are stacked on top of each other. You can regroup any set of paths by going to the Object menu.
Step 2: Tweaking Paths
For example, cutting out a large portion. In the peach colored layer, we want to get rid of the excess above her head. After pulling out the desired layer with the normal selector (usually with traced images it's a little tricky), use the path editor and drag a rectangle over the portion you want to delete. Delete, and we'll smooth out the change. Using the path editor, drag either the edge of the object itself or the nodes/node "arms" to tweak the shape. You can also click individual nodes to delete them. Shift allows you to select multiple nodes at once.
Step 3: Splitting Paths
Step 4: Tweak!
-Get rid of incorrectly colored backgrounds, or just unnecessary layers by dragging them away
- Get rid of details by deleting nodes
- Simplify paths with Crtl + L
Step 5: Save and Export
To export it as an image file, go to File > Export Bitmap
If you export an image as PNG, you may want to create a white object with the Rectangle tool and changing its color to white, depending on if you need a transparent back or not.