I like to cut my slices in half, they could also be left whole or cut into quarters. If you cut it up too small you'll just end up with eggplant mush when you take it out of the freezer later...which is not necessarily a bad thing, just be aware of what you want to use eggplant for in the future. Big slices will be more versatile.
Spread out the slices in a single layer on a baking sheet and put them in the freezer. A Silpat is useful, but certainly not at all necessary.
When the slices are completely frozen they can be transferred to a plastic bag and kept in the freezer for roughly one year.