Curly braces in math mode

Use \{…\}. But, as the contents inside the braces may vary in size, it would be better to use the DeclarePairedDelimiter command from the mathtools package:

\DeclarePairedDelimiter\set\{\}

This defines a \set{…} command, which accepts an optional argument: \big, \Big, \bigg, or \Bigg, which implicitly adds a pair of \bigl…\bigr, &c. in front of the braces. Example: \set[\big]{...}

A \set*{…} variant becomes available for free, which adds implicitly a pair of \left…\right.

You need to escape the braces like \{ and \}.

$K_1 = \{s_1\}, K_2 = \{s_2, s_3, s_4\}$

Also possible to use dynamic delimiter sizing with \left and right, example below.

Calculate the first 4 terms of the sequence below, here typeset
without dynamic delimiter sizing:

\begin{equation}
\{ a_n \} = \{ -(\frac{1}{n})^n \}
\end{equation}

With dynamic delimiter sizing of the curly braces using `\left` and
`\right` the sequence looks like

\begin{equation}
\{ a_n \} = \left\{ -(\frac{1}{n})^n  \right\}
\end{equation}

Off course we can also apply this to the parenthesis

\begin{equation}
\{ a_n \} = \left\{ - \left( \frac{1}{n} \right)^n  \right\}
\end{equation}

Finally, the answer to the question is $\{ -1,1/4,-1/27,1/256,... \}$