The order matters. The bottom tier sits flat on the table, has the largest surface area, and gives you the most slices. Start there.
Before you cut, remove the upper tiers. They sit on cake boards supported by internal dowels (usually wooden food-safe sticks). The dowels are hidden inside the tier below, going about 2cm into the sponge. Lift the upper tier straight up — the cake board comes with it. Set it on a clean surface.
For the bottom tier (typically 10-inch or 12-inch round), cut a circle 4cm in from the outer edge. This gives you a ring of slices. Cut the ring into 3cm-wide slices. Repeat with progressively smaller concentric rings. You will get more slices this way than by cutting wedges.
A long serrated knife works best. Wipe the blade with a damp cloth between each cut to keep the frosting from sticking and tearing.
For the second tier, same process — concentric rings, 3cm-wide slices.
The top tier: traditionally saved for the first anniversary. To save it well, wrap it in three layers of plastic wrap, then a layer of aluminium foil, and freeze. It defrosts overnight at room temperature one year later. Sponge cakes survive this well, fondant survives it surprisingly well, fresh-cream cakes do not.
If you are not saving the top tier, cut it last — it usually has the most decoration and works as the photo cake for the cutting moment.