When your belongings were packed, you should have identified one or two for each room that were priorities for unpacking. For example, bedroom priority boxes might include one set of sheets, a blanket and your bed pillows. Your kitchen priority boxes might include a set of dishes, a pot and pan, your toaster and coffee maker. Unpack those first.
As you unpack each box, cross-reference its contents with your inventory. Check off what you unpack so that you can tell if anything went missing. If any items in the box are broken when you go through a box, take a photo and make note of what the damaged item was. You might need this information if you file a claim for insurance purposes.
When you finish unpacking a box, flatten it. Flattening the box reduces the amount of space that it takes up in your home. Designate a space to pile up the flattened boxes. Alternatively, place them directly into a recycling bin. If you plan to reuse the boxes because you frequently move residences, designate a holding area for them. In order to avoid pests and water damage, keep the boxes off the floor or ground. The boxes could be placed into a plastic storage bin or up on a rafter of the garage.