First time cooking/eating asparagus, what's the best way to cook it?
Snap the hard part of the asparagus, bend the asparagus and it should snap at some point near the harder part. 

Use a peeler to peel the out skin of the stem, the outer skin is tougher, more fibrous.

In all situation, be careful not over cook them, then should still have some bite to them.

Steam or boil, use them whole in this situation.
Pan fry in oil and/or butter, I prefer cutting them in smaller pieces.
BBQ or grill them whole (my preferred way).