If I multiclass a Magus and a Sorcerer in Pathfinder, how do my casting mechanics end up? Do I get a certain amount of slots that I must prepare in advance in addition to a few I can improvise with, or do they all become either prepared or improvised? Do my spell lists stay separate for the different slots, or can they cross over between caster lists?
You retain the casting mechanics of both classes separately.
If you were a multiclassed* level four, such as 2 Magus / 2 Sorcerer, you would have all the abilities of each. Their spell lists do not mix, you will have to prepare your Magus spells, and your Sorcerer castings will depend on castings per day.
*(See Multiclassing header)