A soft, fresh, flaky homemade biscuit is one of the best things there is no matter where you grew up. They're most popular in the South, of course, but they're a welcome piece of homestyle comfort on any plate. Most recipes call for baking powder and shortening, but those aren't mandatory. You can make homemade biscuits without baking powder or with other fats just as easily.
No Shortening, No Problem
Your recipe may call for shortening, but that doesn't mean you can't use other fats. "Shortening" is actually a generic term for whatever fat you choose to put into your baked goods, and it just means that the fat lubricates and softens or "shortens" the gluten strands in the finished biscuit. Vegetable oil shortening only goes back to the beginning of the last century, and before that, people used only naturally occurring fats.
Any fat that's solid at room temperature will work for flaky biscuits, so use what you have and don't worry about it. Lard works well, and butter gives your biscuits a really nice flavor. If you're vegan or baking for a vegan, you can even use coconut oil.
Baking Soda Biscuits
Baking powder isn't much more complicated to replace. If you don't have baking powder but do have baking soda, you're off to the races. Baking soda is an alkaline ingredient, and if you combine it with an acidic ingredient, it reacts to form carbon dioxide and raise your biscuits. Baking powder is nothing more or less than soda with its own acid in dry form.
In baking soda biscuits, you provide the acid separately, usually in the form of buttermilk or regular milk with a bit of vinegar or lemon juice added. A lot of recipes call for both baking powder and soda, so you'll need to improvise a little if you want to make baking soda biscuits with no baking powder at all.
It requires a bit of simple math. Baking soda is stronger, so use just 1/4 teaspoon of soda for every teaspoon of baking powder in your recipe. You'll also need to increase the acidic ingredients in the recipe, so you might find it easier to choose a recipe that's meant for baking soda rather than doing the conversion.
Self-Rising Flour Biscuits
If you don't have an issue with baking powder as such but want to minimize the number of ingredients you keep in your pantry, consider using self-rising flour to make your biscuits. It has the baking powder and a bit of salt already mixed in, so you just need to add the fat and liquid of your choice.
In practice, that usually means self-rising flour, your lard or butter and either milk or buttermilk. That's why you'll often see these described as a three-ingredient biscuit recipe.
Cream biscuits take the basic idea of self-rising flour biscuits and simplify it even further. This is a two-ingredient biscuit recipe, which makes it even more beginner friendly. To make cream biscuits, just stir together self-rising flour and heavy whipping cream. The cream contains enough liquid to hydrate the flour and make a soft dough and enough fat to replace the butter or shortening you might otherwise use.
You can either scoop the finished dough or pat it out and cut it like a regular biscuit. It works fine either way. You can also add a spoon or two of sugar if you like your biscuits a bit sweeter and scone-like.
If you really want to go old school or get away from chemical leaveners entirely, you can go "full pioneer" and make sourdough biscuits. These recipes usually call for the portion you'd remove and discard anyway when you feed your starter, so if you keep sourdough on hand for breadmaking, this is a really good alternative.
Most recipes call for just flour, a bit of fat and your sourdough starter as well as a bit of baking soda just to help the sourdough along. There's enough acidity in your starter to work with the soda as a leavener, and in exchange, the bit of alkalinity from your soda helps the biscuits brown.