What are the Navy Formalities on requesting to come aboard a DDG?

Piping aboard a senior officer is part of the tradition. You proceed up the gangway and stop before boarding. Face aft and salute the National Ensign. Face forward towards the officer/petty officer of the deck, salute, state rank and name, and request permission to come aboard. If in civvies, don't do the salute piece. There will be a be a ding-ding of the ship's bell and "LtCol Army Arriving". Correct procedure is to do the opposite when departing. If there isn't a slew of heavys coming and going, the announcement typically goes over the 1MC (Ships PA) and may be preceded with the low/high pipe pip. Usually on the smaller ships like this one, their Skipper is also an O-5. Good idea to be ready to offer to pay respects if the Skipper is aboard. Your host should know if the Skipper would like a minute. Your title doesn't indicate you are a CO. For those that are, when piped aboard it's "(Name of Command) arriving". Only time for me when it immediately flipped is a change of command when I was piped aboard with the Command name and piped ashore with the rank. It confirmed I was no longer in command. Good ship's crews enjoy the traditions and those who respect them. Enjoy.

You go up to the top of the gang way (unless the Watch is at the bottom of the gangway), stop and salute the ensign, then face the watch, salute, and request permission to come aboard.

This has been answered recently on RP

I am sure you “jg” will take care of you. An O2 on a frigate has a lot of responsibilities. There are not very many officers on a frigate. But those are fast ships and they do go in harms way.

Congrats LTC (Join to see) !!!! Have a great time. Here is the procedure (basically as reported below):
1) The officer that contacted you will more than likely meet you on the pier and give you a brief prior to boarding.
2) If that doesn't happen, keel haul the officer (just kidding)!
3) Walk up the brow. At the top of the brow before you step on to the ship, turn and face the flag on the stern. If in uniform, salute, if in civies just turn face at attention for a second.
4) Then turn to the Officer of the Deck, and request permission to come aboard. He/she will grant permission and then step onboard and towards the greeting party.
5) When leaving, it is the reverse. Turn to the Officer of the Deck and request permission to go ashore while on the deck next to the brow. Once granted, step on the brow, turn to the stern and the flag and salute or at attention depending upon dress. Then walk down the brow.

LTC (Join to see) Colonel, I know our Navy brothers and sisters will also provide guidance.

https://classroom.synonym.com/how-to-board-a-navy-ship-13583557.html

http://navyadvancement.tpub.com/14325/css/Boarding-And-Leaving-A-Naval-Vessel-258.htm

I am coming in uniform. This is a regular work day And to over the 4 officers are active duty army reserve.

I’ve only boarded while in uniform. But we would salute the ensign then salute the officer on deck and request permission to board.

Ships sometimes moor together in port, based on seniority of CO. It's a different situation, but honors and permission remain when crossing another deck to your ship. Request (or I have, for Os) permission to pass vice come aboard. A Lt from our Group was happy in Haifa and asked OOD if he could cross the patio daddio. Didn't even peg the Chief's fun meter. That starts about an hour before liberty expires.