Either obtain ice, or freeze ice packs (the latter are common in the UK, and many campsites will freeze them for you, often for a fee). Larger ice packs will keep partially frozen for 24 hours at moderate outside temperatures, while smaller ones can be tucked in the spaces in a nearly full cool box. If using ice, I prefer to keep it in a wide necked water bottle as not all containers are waterproof. Another solution is to nearly fill a (disposable) water bottle with water and freeze it.
Both ice packs and ice in containers stay frozen a little longer than loose ice, because there's an extra thermal barrier between them and the outside world.
Shade is good, but not if its an enclosed space like a tent, or if it ceases to be shade at the hottest part of the day. Choose wisely. Tree shade is often good, or underneath a vehicle.
An old method is a wet towel over the top of your container, especially if there's a bit of a breeze. You may want to arrange it so the towel hangs into a dish of water to keep it wet unattended. Evaporative cooling is quite effective (similarly you can cool down drinks by wrapping them in wet cloth and leaving them in the breeze). This is applicable in a vehicle too - an open window or cold air vent blowing over the wet towel would help, or strapping the towel round it and putting it in the bed of a truck (it will dry pretty quickly).
Sitting the cool box in shallow running water is another traditional trick - just so long as it doesn't leak.
You don't want to let ice or ice packs touch your salad or fruit, as they will spoil. However these don't need to be kept as cold. Neither do most drinks. Pack those round the outside and in the middle, pack the things that do need to be kept cold (meat, dairy) and your ice packs/containers of ice.
In a vehicle, additional insulation is fairly easy to arrange. Pack the cool box in between tents/kit bags, and you'll find that by the time you get there the outside of the cool box is quite a bit cooler than ambient, demonstrating that the surrounding materials insulate this. On a warm humid day, you can get condensation between the coolbox and the things surrounding it, so be careful; you might not want to place you sleeping bag there.