How does fever physically work?
As John mentioned, pyrokines such as IL1 and TNF affect the hypothalamus. Your hypothalamus is a thermostat, similar to central heating for example. So when you set your core temperature higher, your body thinks it is cold. To warm up it does several things:


Vasoconstriction directs blood to the core body and prevents heat
loss 
Brown fat break down in infants makes heat 
Shivering which requires respiration which produces a lot of heat. Metabolism also
increases in other ways - this is why it is commonly advised to
increase food consumption during illness 
We wrap up warm - an often overlooked mechanism that is incredibly important.  
Limited piloerection: if we are hairy our hair will stand up attempting to
create a barrier for heat loss 
We stop sweating (breaking of a fever or when the hypothalamus is reset to normal causes us to sweat)
Hormonal regulation via (nor)adrenaline/epinephrine, thyroxine - these are related to the increased metabolism.