Break down the cardboard shipping box and place it in your recycling bin. Most curbside programs accept clean cardboard.
Insulation liners vary by material. If your liner is paper-based, it is often recyclable. If it is foam or plastic, check your local program before recycling.
Gel packs can be drained into the trash and the outer plastic recycled where accepted. When in doubt, follow local recycling guidelines for the safest disposal.