How can I keep them alive? By providing them with cultural conditions they are (genetically) programmed to tolerate. You'll need to keep them watered, but lavender doesn't like wet feet (soggy soil), so make sure they actually NEED water before you provide it. Using a homemade device made from a wooden dowel rod (less than $2 from any hardware) would be helpful.
Should I keep them in the full sun? They are a full sun plant, meaning they'll do best in full sun. If when you bought them they were in full sun, they are acclimated to full sun and it would be best to provide them a spot where they continue to get full sun. If the plants were under cover (in a greenhouse or hoop house) you might want to protect them from full midday sun; though it's hard to imagine how/why they wouldn't already be acclimated to full sun.
Should I water them often? See "Using as Tell" below. I am concerned about them dying because I don't have experience keeping things alive in pots before transplanting them into the ground. If you were to err, it would likely be on the side of over-watering, and you'll know how to deal with that in a bit, after reading the "tell" thing below. You probably won't need to fertilize unless you start to see old leaves are falling off. If you do notice that occurring, it could be associated with with low fertility, especially nitrogen. We can deal with that if it becomes an issue. If you see little round balls about the size of small peppercorns on the surface of the soil, you won't need to worry about fertilizer. That will be a controlled release fertilizer designed to release nutrients slowly over a long period.
One of the most reliable methods of checking a planting's need for water is using a 'tell' (more reliable than a 'moisture meter'. You can use a bamboo skewer in a pinch, but a wooden dowel rod of about 5/16" (75-85mm) works better. They usually come 48" (120cm) long and can usually be cut in half or in several pieces, depending on how deep your pots are. Sharpen both ends of each tell in a pencil sharpener and slightly blunt the tip so it's about the diameter of the head on a straight pin. Push the wooden tell deep into the soil; all the way to the bottom of the pot is best. Don't worry, it won't harm the root system. If the plant is quite root-bound, you might need to try several places until you find one where you can push it all the way to the pot's bottom. Leave it a few seconds, then withdraw it and inspect the tip for moisture. For most plantings, withhold water until the tell's tip comes out nearly dry. If you see signs of wilting, adjust the interval between waterings so drought stress isn't a recurring issue.
Al