When your refrigerator garden is newly planted, you will need to water it every night until the plants are established, using a watering can; just a couple of gallons is more than enough for a larger refrigerator. After a few weeks, you may be able to reduce your watering cycle to watering every couple of days, but the best rule is to stick your finger 1 inch into the soil and see if it's moist. If the top looks dry, but is moist underneath, you might only need a dribble of water. Learning the watering schedule for your garden takes time, but if you start to notice your plants have yellow leaves or limpness, then you might be watering too much. Brown dry leaves or limpness could mean not enough water. It takes a little practice, and depending on the weather, you'll have to change your watering cycle, but pay attention to the plants, and they will tell you what they need.
Water the soil, not the plant leaves, and it's best to water in the evening or before the sun is high in the sky in the morning, otherwise, any water on the leaves will burn them in the sun.
When you're watering, you want to avoid beating the plants up too much or getting water on their leaves. You can gently disperse water from the watering can on the soil for small seedlings with your hand. As the seedlings grow larger, pour the water gently using the watering can. To extend your growing season in the colder months, you can use warm water, make sure it's cool enough that you could comfortably hold your hand in it.
You can also use water-soluble fertilizers; see more on the fertilizing page. If your plants seem unhealthy, no matter what you do, your water pH may be out of balance, consider getting a pH test or using bottled water to feed your plants.