You breath it out, for the most part. Fat is "burned" to convert the carbons to CO2, which is breathed out. There's not very much fat-derived carbon in each breath, but you breath a lot, all day long.
At rest, an average 70 kg person consuming a mixed diet (respiratory quotient 0.8) exhales about 200 ml of CO2 in 12 breaths per minute. Each of those breaths therefore excretes 33 mg of CO2, of which 8.9 mg is carbon. In a day spent asleep, at rest, and performing light activities that double the resting metabolic rate, each for 8 hours, this person exhales 0.74 kg of CO2 so that 203 g of carbon are lost from the body. ... Replacing one hour of rest with exercise that raises the metabolic rate to seven times that of resting by, for example, jogging, removes an additional 39 g of carbon from the body, raising the total by about 20% to 240 g. ...
Our calculations show that the lungs are the primary excretory organ for fat.
--When somebody loses weight, where does the fat go? Ruben Meerman and Andrew Brown, BMJ 2014; 349