Let us just say that the most important factor, the one thing that no plant can live without is DRAINAGE! Actually, there are a few other factors, but without good drainage your plant will die from rotten roots. There's a lot going on at the roots: The plant is taking in nutrients, breathing, and standing up. (It's as if we were buried to the waist upside down - if that makes any sense to you)

Run-off is a natural consequence of good drainage. Unless you're using self-watering pots, to take care of your plants, you will most likely water until you soak your soil, which means you will water until water pours out of the bottom of your container. We repeat, this means water will pour out of the bottom of your container. Plan for this run-off. Love it. Collect it - use a turkey baster if your plants are too big to move.

If you don't want water running everywhere, use catch basins under your pots. High-sided saucers work very well. You can improvise (pie tins, or find suitable saucers at your local thrift store) or you may buy custom-made basins.

In order for your container to drain properly into the catch basin, make sure that there is air space between the bottom of the container and the basin. Use rocks, pencils, or whatever you can find to prop the container up slightly, and allow the water to flow.

Keep in mind that catch basins are just there to catch the water - not to hold it there. (Otherwise, they'd probably be called hold basins.) DO NOT let your pot sit in water in the catch basin - that defeats the whole drainage process. 30 minutes after watering, make sure the catch basins are empty.