Chile is 3000 miles long and about 100 miles wide, and the climate varies greatly from one region to the next. Also, in some regions of Chile, the seasons are not entirely predictable, so please take the following as a guide and be prepared for changes in climate.
Many people traveling to Chile will be heading to the spectacular region of Patagonia at some point during their stay. Patagonia has weather like Alaska, with a mix of sun, rain and wind on almost any given day. From October to mid April the temperatures vary from the 40s to mid 60s during the day, sometimes a bit higher for stretches when the sun stays out. At night it will typically be in the 30s but can drop down into the 20s. The wind in Patagonia is highly variable, and you should be sure to pack some type of shell over layer or other wind protecting jacket.
Santiago, the Chilean capital, has a Mediterranean climate, with an average daytime temperature in the low 80s in January and about 50 in July (the middle of their winter). The dry season is September to April and the wet season is May to August.
The Lakes District has a climate like the Pacific Northwest of the United States, but with the seasons reversed. The best time to visit is from October to April, when there is a pleasant mountain climate. Rain can still fall during this part of the year, but it will generally be short-lived and much of the day will be clear. The wet season is from May/June to October, and it rains fairly predictably and consistently during these times, though there can be periods of better weather.
In Atacama and the northern deserts, the climate is hot and dry all year, in the 80s and 90s during the day and cooling off quite a bit at night. the Atacama desert is the driest place on earth, and there are places in the region where there has never been any recorded rainfall.