What is the best approach for elbow arthrocentesis?

Lateral.

1. Prep. Anesthetize.
2. Flex elbow 45 degrees.
3. Pronate hand.
4. Identify depression between the lateral epicondyle of the humerus, the radial head and the tip of the olecranon process of the ulna.
5. Insert needle perpendicular to skin. Aspirate.
   

Source

Reichman, E and Simon, R. Emergency Medicine Procedures

Image source: http://emedicine.medscape.com/article/79975-treatment