Can every DFA be simulated by a PDA?
I hope this answer will help you to understand the mapping. Any DFA is also a PDA. The state transitions in the DFA are similar for PDA without stack. For every transition you perform in DFA, make the similar transition in PDA and do not push/pull from stack. 

For a transition 

In DFA : $\delta(q_x,0) \rightarrow q_y$

In stack : $\delta(q_x,0) \rightarrow (q_y,\epsilon)$

For accepting state

In DFA : $\delta(q_x,0) \rightarrow q_f$

In stack : $\delta(q_x,0) \rightarrow (q_f,\epsilon)$