1) Some things are likely to be boxed or binned already. If they're labeled, take a peek inside to see if the contents match the label. If not, relabel. If it's unlabeled, take a look. Without going too deep inside, label the box with what you generally see in there: Memories, Games, Clothes, Photos, Toys, etc. These labels might only be temporary, so sticky notes may do the trick.
2) Start making those categories! Get boxes, bins, bags, and loose items near each other that are like-items. All the bins with clothes and the loose coats laying around get stacked up near each other. Same with toys, electronics, whatever else you're finding in there.
3) Take a break! (Remember: timing and energy level are important things to be aware of!)
4) Time to come back: Tackle one pile at a time. This time around, go through the boxes in depth. Pull everything out so you can see all of the category. Are these items you use (probably not if they're in lost storage areas - or at least not used often)? Are they items you love? Are they enhancing your life in some way? Have some empty bags on hand for trash, recycling and donations.
5) Repack and relabel. This time, you might consider labeling boxes more in depth: Johnny's memories; Toys from Childhood, Photos from Mom's House.
6) Stack or shelve accordingly.
7) Start at step 4) for the next pile. Depending on time and energy, it's fine to take breaks between categories.
Enjoy you're newly organized storage!
