How do i propagate succulents without making a mess?

The step most people get wrong is watering too soon. Wiggle a leaf side to side until it pops off with the little base intact. If it tears and leaves part on the stem, it won't root. Leave the leaves on a dry tray out of direct sun for a few days until the broken end has dried and sealed over. Then lay them on top of a gritty cactus mix, don't bury them, and don't water. Once tiny roots or a baby rosette show up, mist the soil every few days. Water before that and they just rot. Doing it all in one seed tray keeps the mess in one place.