Fahrenheit equals Celsius times 9/5 plus 32. Temperature is the one conversion on this site with no factor at all: the two scales have different zero points as well as different degree sizes, so you cannot simply multiply. Getting that wrong turns 20 °C into 36 °F instead of 68 °F.
About the units
Daniel Gabriel Fahrenheit published his scale in 1724, anchored on a freezing brine mixture at zero and roughly human body temperature near 96. Neither anchor survived scrutiny — body temperature landed at 98.6 °F once the scale was tidied up — but the scale stuck in the English-speaking world. Anders Celsius proposed his in 1742 in Uppsala, and his original version ran backwards: 0 was the boiling point of water and 100 the freezing point. It was inverted shortly after his death, by whom is still argued over, and the inverted form is what the world uses. Both scales are now formally defined through the kelvin: a degree Celsius is exactly the same size as a kelvin, offset by 273.15, and a degree Fahrenheit is exactly 5/9 of that size.
The exact factor
The formula is °F = °C × 9/5 + 32, or equivalently °C × 1.8 + 32. The 9/5 comes from the degree sizes: there are 100 Celsius degrees between the freezing and boiling points of water and 180 Fahrenheit degrees across the same interval, and 180/100 = 9/5. The 32 comes from the zero points: water freezes at 0 °C but at 32 °F. Because there are two operations rather than one, the usual shortcuts fail — you cannot convert a temperature difference the same way you convert a temperature. A rise of 10 °C is a rise of 18 °F, not 50 °F, because the offset does not apply to differences. One elegant consequence of the arithmetic: the two scales cross at −40, which reads the same on both.
Where you meet this conversion
Weather is the everyday case, and the two scales differ enough that a misread forecast means dressing for the wrong season. Cooking is the risky one: an oven set to 200 °F instead of 200 °C will not cook anything, and 350 °F — the default American baking temperature — is 177 °C, usually rounded to 175 or 180 on European dials. Medicine uses both, with normal body temperature at 37 °C or 98.6 °F and the fever threshold around 38 °C or 100.4 °F. Industrial and scientific work has largely standardised on Celsius or kelvin, but American engineering documentation still carries Fahrenheit in places.