I have a drain that has a trap.. it is in the rafters above the washing machine, do I have to run the pipe down, then out and up for it to drain? Not sure what to do... please advise

You want to know how to plumb the washer into the existing drain you see above? You need to tap into it at a point that is below the top of the washer, preferably as close to the floor as possible. The 'stand pipe' should be about 30" long, several inches of which are above the washer, have a trap on it, and then slope (min 1" in 4') to the main drain, which can't be more than about 5' away. All of this will have requirements that vary by local code. Your hardware store might know, or you will have to call the building inspector. Hopefully your drain (stack, waste, or DWV which stands for drain/waste/vent) isn't cast iron?

Rafters hold up the roof, joists hold up floors.

Joypulv is right. It always looks easy to hope you can just stick the pipe in the drain and it will work, unfortunately, water doesn't flow up and you would also have a backwash. Unless you have floor drain access or a waste line at or near floor level or a lift pump, you will find it difficult to install a drain system.