If you're out in the wild, start off by making your own shelter. There are plenty of ways to do that. Refer back to one of your first Basic Survival lessons. You can make your own shelter out of sticks, grass, moss, and the likes. Unless you're not in a forest setting but in a desert one, you can make this type of shelter. If you're in a desert, then you're royally screwed. Refer to the pictures below and your knowledge. It may not be very comfortable to be on the wet and soggy forest ground, but you'd rather be protected and blend in with your surroundings than stick out and be cold.
If you're still in the city and don't want to build anything, there are still some ways to take cover. These might require a bit more traveling and asking around the city to find, but it's ultimately worth it. Depending on how populated the city is, these may vary. Religious buildings such as monasteries, priories, and churches may offer shelter during the night. They offer more as well! Occasionally, they will offer free food to the homeless and those in need as well as clothing through donations. Take what you need, but don't be greedy; these are services for everyone.
Lastly, alleyways can also be used as a shelter. Many dumpsters have a lid you sit or crouch underneath, though keep in mind about the stench. (New York especially, it’s unbearable.) But, if you're desperate enough to consider this option, chances are the smell will be the least of your worries. Bridges also can keep you out of the rain and are really everywhere in the country.
That's all for this edition. Be careful and remember to lay low, as you can be charged a fine for sleeping in public - as ridiculous as that sounds - in some cities. When in need, the law is really your last worry as a demigod.