Is there an algorithm to find all subsets of a set?

I'm trying to find a way to find all subsets of a set.

Is there an algorithm to calculate this?

The algorithm in a recursive one. To understand the algorithm consider the following example:

Let $S = \{1,2,3\}$. The subsets of $S$ are all subsets of $\{1,2\}$ and all subsets of $\{1,2\}$ with the element $3$ appended to each subset. Essentially, if you know subsets of $\{1,2\}$, the problem can be solved. You can take it from here on.

An alternative to the recursive formulations provided so far to enumerate the subsets of a finite set is to index the subsets : if $n$ is the number of elements of your set, there are $2^n$ subsets. The subsets can be enumerated iteratively by using a variable index ranging from $0$ to $2^n-1$, and using the binary representation of the variable index to determine which elements of your base set the current subset has.

Over recursive formulations, this one has the advantage of not risking a stack overflow, which may happen if $n$ is greater than the stack capacity. It also avoids storing lists of subsets if you can process these subsets with a continuation.