Good hotwire technique is an art I'm still trying to perfect. In general, I can say that the cut surface is much smoother if you don't let the wire snag on anything and if you try to make sure you move the wire with relatively consistent speed. If the wire snags, often this can result in a deep groove where the wire burns into the surrounding foam as it sags. if you can keep it moving that keeps tension on the wire and makes the cut more predictable. Doing a few practice cuts is a great idea; after you cut 4 or 5 random little pieces you start to get the hang of it and will certainly be able to do this project. If you want to make your own hotwire you should check out the instructable
Hot Wire Foam Cutter.