Any tips to help this process? Which side do I start first and the hardest part is holding the entire thing up while I'm trying to line everything up.

 

Im assuming your bike is on a rear stand. Put the chain on the sprocket, sit behind the bike, take one of your feet and place it under the rear tire so you can lift the tire up into place with your foot. then slide the axle into place.

 

^There must be some little trick because when I try to put the rotor in the caliper it has doesn't want to go in.

 

The bike needs to be on a stand, push the pads back in the caliber a bit (widen) the gap so the disc will slide in. Take a screwdriver and pry them back inbetween the brake pad material not on the material itself. insert sprocket and rubber cushions, chain then the 2 washers. Get a pry bar and stick under the tire then lift up a extra person would not hurt, i do it by myself. That is the same for a 600rr and a 1000rr. hope this helps