One of the most important things a new plant owner needs to be aware of is overwatering their new plant babies. The other is watering erratically or not at all. Death by drowning or dehydration isn't on my top 5. Appropriate H2O is one of the keys to happy plant parenting, ensuring many years together.
Plants have different needs when it comes to hydration. Understand your plants needs, and instead of sticking to a strict - every Sunday at noon - watering schedule, observe the soil. Is it dry? If so, it's likely time to water.
Your particular environment (dry house, sunny window sill, cold drafts) will all impact the soil, and thus your plant and the watering schedule.
Containers matter. Pottery without drainage holes will often hold excess water, giving the plant "wet feet"; unless your species enjoys this spa treatment, it's best to look for pottery that allows excess water to run out to avoid root rot and other unpleasantries that can arise.
Always water at the base of the plant, which is especially import for succulents and cacti, and not the leaves. Be thorough when you do water to ensure good hydration between waterings.