Why’d you come in the first place? Resource extraction, cultural research/exchange, scientific research, missionaries for THE ONE TRUE UNIVERSAL GOD, slaves? Different motives have different answers. Research and educational motives would lead me to try to remain inconspicuous. Everything else would follow the “Independence Day” method. Don’t need to pull the trigger if not needed.
I would deliver my message:
“People of Earth. Meow. We bear glad tidings. Meow. There is a simple secret to life. Meow. Which will ensure your survival in they upcoming trying time we foresee for your planet. Meow. It is…”
Five minutes of static and pops and unintelligible sounds, meow.
“… Meow. And that is what has made all the difference to our people. Meow. And shown us the way to the stars. Meow. As long as you always remember that…”
More static.
“…you will also prosper. Meow. Our time here is short and we must now go. Meow. But, should you heed our words you undoubtedly will soon join us in the galactic brotherhood.”
“Meow”
Or, they could make their presence very obvious and well-known and (seemingly) benign, if their true agenda was Serving Man.
Or we could go the Douglas Adams route – land in front of a yokel out in the middle of nowhere, walk around making space-alien noises, then leave.
Or the other Douglas Adams route: General demolishment. 
I would set up a research outpost, staff and equip it as necessary to study the planet thoroughly while remaining undiscovered, and leave, with a promise to come back after an appropriate interval.
However, as I am a devious asshole, instead of picking up the research outpost staff when I come back, I would first extract all the data they have collected, and then disable their stealth technology so as to reveal them and all their works to humans. This would reveal a great deal about how humans deal with sudden change and potential danger. The staff of the outpost may end up getting killed, but the process will be a tremendous addition to our knowledge of this species. That is the kind of culture I come from, after all.
My report to my superiors:
"*Sir, we investigated the oceans first and discovered Earthlings there. We remain puzzled by their relationship with the planet’s water.
They move about on machines known as “cruise ships”, but with no apparent transport purpose. While cloaked, we observed their behavior up close and can make no sense of it. They seem to abhor the water around them and construct the machines to ensure no contact with it. Then for reasons unknown, they have built large tanks of water on the ship’s decks, within which they splash around. But when perfectly good water begins falling from the sky (a regular occurrence on Earth) they immediately flee below decks to individual tiny boxes. And here it gets weird, they disrobe and enter a tiny sub-box within their individual box and stand under pipes which dump water on their heads. We remain confused, and humbly request permission to try another planet.*"
I totally want to meet Kristen Johnston, John Lithgow, & French Stewart!
“People on that spinning blue ball, sorry to blow your minds. No reason to freak out. It’s just that it’s been, like, over four years since we’ve had a report from Special Agent Ziggy Stardust. Just let us lay eyes on him, man, and everything will be cool.”
This is fantastic.
Indeed it is.
Has any science fiction ever depicted aliens appearing to act in weird ways like this?
Playboy Mansion, Krispy Kreme, then bounce out of this galaxy.