The best way to pack your luggage!

Do not pack flat. Roll your clothes up, with the most compressible and softest clothes in the top layer to be squished down by the lid. This technique allows you to maximally compress all your clothes without wrinkling them.

Place shoes and hard objects on the bottom. Place items that might be crushed or broken on the top among the soft clothes. Place overflow items in side compartments; they exist for a reason.

Buy a maximum size wheeled carry-on as well as a large backpack or small duffel bag. The wheeled luggage can be valet checked to avoid checked bag fees. The other bag goes on the plane with you.

Buy a coat with large pockets. This doesn't work if you want to dress nice and get a first class upgrade, but otherwise you can generally get away with putting extra books and small boxes in the pockets. This is great if your bags are completely full but you just have three books you think you'll be switching between in-flight.

Pack less. You don't really need a week's worth of clothes for a weekend. You don't really need to ensure that you won't need to do laundry before getting back a month later. Do you really need every school textbook? How many snacks will you actually eat on a 3-hour flight?