If you live in goat head thorn areas, you are already familiar with much of the drill.
When it comes to camping, there are a few things I add to the discipline:
1. As much as possible, I hang out on the major roads. That short-cut sidewalk or trail might seem tempting, but it might also have a lot of new thorns.
2. When I go to my campsite, I will often carry my bike rather than wheeling it. If I stop along the way to go to the bathroom, I might also be careful in how I transport the bike.
3. Before getting back on the road (I will have carried the bike), I'll also carefully check each tire making sure no goatheads have attached themselves.
4. When using a thermarest or similar inflatable mattress, check twice under the tent site to clear out thorns. Consider using a ground sheet. Might not stop them completely, but probably also helps.
I do end up with more thorn-resistant tires like Schwalbe Marathon Plus. At least when new, these can definitely help - though they also aren't 100%.