Saddad's method works excellently for me too, but you can also divide and share a little earlier in the season if you want to.
As soon as you see the sheathed leaf buds just break the soil, you can have a little scuffle in the soil around; they have fleshy roots and as long as you get a decent bit for each leaf bud they've always been fine when I've done this for give-aways. As the leaf buds are quite snappable at that stage, spread them out in a pot/ food tray/ seed tray rather than a poly bag.
My lily-of-the-valley do me proud. In return, the poor things get a diet of shade, clay soil, neglect and (till this coming season) not much water either, as they've been growing at the feet of a sprawling juniper which I hacked down at the start of winter. They'll probably all faint and die at the shock!