Watering
I’ve read a lot of different opinions on this topic. Basically, just keep the soil moist but not saturated. It’s ok to let the soil dry a little between waterings as long as the plants don’t wilt too much. The only time over watering is really a problem is when the plants are young and don’t have a good root system yet. That’s when they just sit there in the mud and eventually turn brown and rotten. Too much water in the winter will also hurt them. Just watch the plants and they’ll let you know when they’re thirsty.
Fertilizing
You can fertilize Salvia Divinorum with whatever you want. There’s no magic fertilizer that they like best. Miracle Grow has always worked well for me. I give them a light dose about once a month. Basically, just water and fertilize them the same as any other houseplant and they’ll do fine.
Soil Mix
A good soil mix for Salvia is one with some organic material, peat moss, vermiculite, perlite and a little sand (Soil Mixes). Once again, there’s no magic formula. Most commercial mixes work well; just avoid the cheap black potting soil. The key is to make a mix with good drainage and lots of air. I've seen beautiful Salvia plants grown hydroponically as well, but I have no experience with it. I've always preferred soil.
Pests
Pests will probably be a problem at some point in time for you. Spider mites and whiteflies seem to love these plants. It only takes a few of them to start causing leaves to curl and turn yellow. My best advice is to keep a VERY close eye on your plants and take care of any bugs quickly to prevent an infestation. Once you have bugs either remove them with your fingers or use a spray bottle with water and a drop or two of Ivory soap in it to keep them away. Neem oil also works well as a preventative; just use it about twice a month and most bugs’ stay away (Read about using Neem).
Cloning
Taking cuttings is pretty much the only way to make more plants. I don’t recommend taking any cuttings until the plants are at least a foot tall and have several branches. If your plant has only one main stem wait until new branches start forming before topping it. Taking cuttings from an immature plant will usually result in rotten cuttings and a dead mother. I still haven’t had one of my plants flower so I have no experience with growing from seed. The bad part is that Salvia cuttings can be hard to root and many cuttings won’t make it. You’re best bet is to take a lot of cuttings and hope just a few make it. (Some’s better than none!) Another tip is to only take cuttings from actively growing plants. Plants that aren't growing leaves probably aren't going to grow any roots either if you try rooting them.
Rooting in Water
Salvia will root in water fairly well. Just take your cuttings and stick them in a glass or jar of clean water. Sit them on a windowsill or under lights and they should have roots in about 10 days. Make sure to change the water often so the stems don’t get rotten. If the stem starts turning brown and the discoloration moves up the stem, the cutting is a lost cause. This rot is the most common cause of failure that I’ve seen when trying to root cuttings. I try to keep the cuttings in different cups so that if one gets rotten it doesn’t spread to the other ones. Once a cutting has a bunch of roots, take it out of the water and plant it into some moist soil. It’ll need some TLC for a few days so keep an eye on it to make sure it isn’t wilting. This is a time when misting is actually necessary. Another thing you can do if you live in a dry area is to cover the glass with a baggy to help keep the cutting from losing too much water.
Rooting Directly in Soil
This method also works well, sometimes... Take your cuttings and stick them directly into a moist soil. Mist the cuttings often and they will usually start to root within 2 weeks. The only problem I’ve had with this method is more stem rot. Maybe sterilizing the soil first would help, but I’ve never tried it. First, you get some clean trimmers and take the cuttings. Now you get yourself a flat and stick the cuttings into the soil. Next to the flat is the mother plant after being trimmed. An optional step is to use rooting hormones (IBA). I dipped one just for the picture but I didn't use any on the rest of the cuttings. I'm still not convinced that hormones make this particular species of plant root any better. Next, I put the flat under a fluorescent light and kept the humidity high (around 70%). Some things that could be experimented with to increase success are taking varied cuttings. I've noticed that smaller cuttings tend to do better than larger cuttings. Using rooting hormones may also increase success but I've never observed that they really made that much of a difference.
I guess the best advice is to keep trying until you find a method that works best for your plants. I usually use the glass of water technique because its easier, cheaper and usually works. Putting the cuttings into soil requires more work to keep the temps and humidity within range, and often results in more lost cuttings. Some plants such as Cannabis love to root right in the soil, but Salvia plants can be a little touchy.