This herb grows easily in any normal garden soil. Propagation is by seed, root division, or stem cuttings. Root divisions can be done in the spring or fall, but if doing in the fall, do it early enough that the plant can establish itself before freezing weather hits.
If left alone, meaning not prunned to get the best flavor, the plant goes to seed and will spread itself in places you may not want. Some gardeners don't like the plant because of that quality, but I find it's not hard to keep in place, and even if a plant comes up in a bed where it doesn't belong, it's easy to pull out. My chickens always enjoy an airborn plant that lands in their yard and they eat nearly every part of a lemon balm plant, leaving only a few stems when they are through.
Lemon balm will withstand drought better than some herbs, although if grown under stress, such as with very little water, it goes to seed quickly and the flavor changes. To prevent this, use scissors or pruners and cut the plant back half-way fairly often. It is the tender, younger leaves that have the tasty lemon flavor. The old leaves, particularly when the plant is blooming or producing seed, have an almost unpleasant, soapy flavor. But the fresh, tender leaves are delicious.
Lemon balm grows best in average garden soil, with normal moisture. It will take part shade or full sun. I have one that lives next to the rhubarb, which shades it midday and late afternoon and it seems very happy there. I often combine the lemon balm with rhubarb in recipes, as well, since they are such good companions in the garden.
Lemon balm is best used fresh but you can also dry it for use later. I dry mine in the food dehydrator, on low setting. Sometimes I grow it in a brown paper bag, a couple of handfulls of the herb inside. I clip it closed with a clothespin and keep it in the trunk of the car. If I think of it, I shake the bag every 2 or 3 days and within about a week, the leaves are crisp and it's ready to store.
Store dried lemon balm in an airtight container in a dark place, such as pantry or kitchen cabinet. If I have a lot of dried lemon balm, I double-bag it and keep it in the freezer and that seems to preserve the flavor really well. Just remember to make sure the herb is completely dried before you put it in the bag.