How to convert formula to disjunctive normal form?

You can continue by using Distributivity of the boolean algebra:

$((¬p \vee ¬q) \vee r) \wedge ((p \wedge q) \vee r)$

$ \Leftrightarrow (¬p \vee ¬q \vee r) \wedge ((p \wedge q) \vee r)$

Here we apply distributivity:

$ \Leftrightarrow (¬p \wedge p \wedge q) \vee (¬q \wedge p \wedge q) \vee (r \wedge p \wedge q) \vee (¬p \wedge r) \vee (¬q \wedge r) \vee (r \wedge r)$

Formally, this is in disjunctive normal form now. We could further simplify:

$ \Leftrightarrow (r \wedge p \wedge q) \vee (¬p \wedge r) \vee (¬q \wedge r) \vee r$