Houseplant care is pretty easy. If you understand the basics and are consistent in applying the basic principles, your plants should look nice and healthy and you should be able to fully appreciate the joy they bring.
Before I start, it's important to remember that there are thousands of different plants and each one has slightly different needs. It's a good idea to read about the plants you have to see if they have any special requirements. Some plants are fussy (such as orchids) while others are very forgiving (like the Pothos plant). But either way, a quick Google search should tell you enough to get started.
As you know, water is the lifeblood of plants. Knowing exactly how much water to give a plant isn't always easy. It can vary from season to season and from plant to plant.
Cacti and succulents are geared for growing in deserts. They only need very little water (water them once every couple of weeks).
Orchids are from the tropics, and like to be watered as if there were a tropical thunderstorm. That means you should give them a soaking water and then let the soil dry.
Many houseplants aren't as fussy as this, and will be perfectly happy to be watered every day enough to keep the soil moist. This is my general advice.
In winter when your plants get less light, they won't need as much water. So you should adjust accordingly. When you find standing water in the saucer at the bottom of the pot for long periods, you're probably giving them a bit too much water.
When you go on holiday, have a ready through my page on vacation watering for some handy tips to keep your plants fed.
Water isn't the only food that plants need. They also need 13 mineral nutrients. The primary nutrients are Nitrogen (N), Phosphorous (P) and Potassium (K). Fertlizers (also called Plant Food) are labelled with an "NPK" number that indicates the ratio of these three elements contained in the fertilizer.
A good potting soil will contain some of these required nutrients, but you should fertilize every couple of weeks to replenish them. You will notice the difference!
Different plants prefer these primary macronutrients (N, P and K) in different quantities. That's why you'll see lots of different types of plant foods. As a beginner gardener, I'd recommend just picking up a general purpose plant food. And a word of warning -- plant food stinks so it's best not to use it just before you have guests!
A key aspect of houseplant care is making sure plants get the light they need. You'll need to find out if your plants like full sun, partial sun or shade. Herbs for instance generally like full sun. If you put them in a dark spot, they will wither and die.
Window sills are great places for growing full-sun plants. Bathrooms are ideal places for plants that like being in the shade.
If you want to grow more full-sun herbs and veggies than you have window-space for, or if you live somewhere where the plants won't get their full dose of sunlight, you should investigate using artificial grow lighting. These are lights that produce light in the spectra that plants use.
The key thing to remember regarding pests is that you should deal with them as soon as you notice them. Although gardening indoors is less prone to pests and disease than outdoors, there are some indoor gardening pests that you should know how to treat. The linked-to page also has recipes for some home-made organic pesticides. Check your plants regularly for any signs of disease or pests, and deal with it immediately!
As you become a more experienced gardener, you'll get to know more about your specific plants and general houseplant care.