So, climate describes the long term pattern of weather conditions that occurs in a locality. Thermometers and rain gauges are used to collect weather data. These days temperatures are also taken by satellites to reduce the possibility of false high readings due to heat in cities. We can't take Earth's temperature directly, but we do have a lot of information from weather stations, ocean buoys and remote sensing instruments. The information lets us see changes in climate.
An ice core.
Each layer in an ice core tells scientists something about Earth's past.