Take a clause "a OR b". This says at least one is true. Flip it around to see the implications. If a is false, then b is true to satisfy the clause. If b is false, then a is true. In graph terms: add edge (NOT a → b) and edge (NOT b → a).
These two edges represent the OR constraint perfectly. Every clause in your formula becomes exactly two directed edges in the graph. The graph has nodes (for n variables) and edges (for m clauses).