How do I get to the cinema? How can I get to the cinema? Are they both correct?
Can I ask for directions using both, or is " How do I get to..." more common? Thanks :)

Question

Answer

They are both grammatically correct.  However, to get directions, you'll want to use "do".

The use of "can" implies you are asking about forms of transportation.  For example, some replies to "How can I get to the cinema?" would be:
"You can walk."
"You can take the bus."
"You can drive your car."