As per question title, how does it work? What are the differences of being in a party or playing alone? Does it apply to finding orbs?
Magic Find is calculated using the Increased Item Quantity(IIQ) and Increased Item Rarity(IIR) of the player that gets credit for the kill. If a minion gets the kill, then any IIQ/IIR from support gems affecting that minion are applied first.
From my experience this also affects opening chest, so when we go out in a party, we usually have the person with the highest MF open the chests.
I think IIQ is the only stat that will give you more orbs, while IIR increases the rarity (color) of an item.
Edit Thanks to Kexlox for finding this information on IIQ in parties:
Source: Mechanics Thread