Even the best gardeners find themselves with the occasional sick-looking specimens, and if you want to save your dying plants, the first step is to figure out what's causing the problem. Only after identifying the problem can you hope to fix it. The most common plant problem by far is watering. Usually under-watering is the culprit, but sometimes you can get carried away and over-water instead. Either can be fatal to the plant.
All plants require some level of moisture in the soil. Their roots act as wicks, drawing up nutrients and water together from the soil. Without water, they simply can't get nutrients out of even the richest soil. If there's too much water, on the other hand, the roots can't get enough oxygen and will suffocate (yes, roots breathe too). That can be even more hazardous to the plant than a lack of water.
If your plants are looking limp and droopy, they probably need more water. Stick a finger into the soil near the plant's base, and if it's dry, you definitely need to water more. Keep watering every day or even twice a day if the weather is extremely hot and dry. A slow, deep watering is ideal, since it gives the roots more time to grab hold of the water. In a few days, the plants should start to perk up and hopefully produce new leaves.
If your plants are drowning, you need to draw off the extra water and reduce the amount they receive in the future. For outdoor plants, this may mean digging a drainage ditch to lead the water away. For indoor plants, just cut down on the watering. Don't water unless the soil is dry an inch down, and then water until you see it just start to come out the drainage holes in the bottom of the pot. If the container doesn't have drainage holes, that's the likely culprit. To fix this, drill holes in the pot or transplant to a new one.
When adjusting the water level doesn't do the trick, the next step is to check for symptoms of malnutrition. Generally plants suffering from a lack of nutrients will change leaf color. Most nutrient deficiencies cause them to turn yellow, but others will cause dark green or reddish-purple leaf colors. Treat plants immediately with a water-soluble fertilizer, following the directions on the package. Organic gardeners can use compost tea instead, or even old half-strength coffee (it contains plenty of nitrogen, as well as micronutrients that are like plant vitamins). Once the plants recover, continue to feed them regularly with high-quality compost or fertilizer.
If none of these treatments work, you probably have a disease or pest problem. Pests usually make themselves known by chewing holes in the plant's leaves and/or stems. Treat with a broad-spectrum pesticide and monitor closely. Disease problems are usually best treated by trimming off all the infected tissue, feeding and watering well, and making sure the plant gets plenty of light.