Weather
Weather describes the conditions of the atmosphere over short periods of time. For example, you might say, "The weather in Seattle is sunny today." At any given moment, weather can change and alter the way you view or describe the atmosphere of a location.
Climate
Climate refers to the weather patterns that occur over a long period of time. For example, even though Seattle might have a sunny day, its overall climate is rainy. Climate does not change rapidly; the way you describe the climate of a place is unlikely to change from day-to-day.
Climate Change
If atypical weather patterns persist for a long period of time, then it can be said that the climate is changing. There is no official time span for establishing whether or not the weather has changed enough to constitute climate change. While some would say that a year with record high temperatures could be indicative of climate change, others would only apply the term climate change when unusual weather has occurred for a decade or longer.
Correct Use of Meteorological Terms
When describing the day-to-day changes in atmosphere, it is appropriate to use the word weather. Remember that just because a place has a rainy day, or even a rainy week, it does not mean that it has a wet climate. Use the word climate to describe general weather patterns, understanding that from time to time there may be some variation. This does not necessarily mean that the climate is changing, only that the weather has been unusual.