The market unlocks and opens for business at 8:00AM. However, merchants will begin selling their goods at 7:00AM even if they have not entered the marketplace yet.
If you come to the marketplace in the morning (around 8:00 or 9:00 AM), some of the merchants will be eating breakfast at Gary's Galley. The guards will say things along the lines of "* merchant* is eating breakfast right now at the Gary's Galley, but they will still sell to you, just ask.".
You can get a key to the marketplace by pickpocketing or killing a Rivet City guard and looting their corpse (both resulting in negative Karma). The key is called the "hangar key". Alternately, you may pick the Average lock. The single door leading out to the broken section of the ship is locked with a Very Hard lock, and needs Harkness' key to unlock.
If you are in the Rivet City Marketplace just before closing time people will warn you; if you do not leave, the entire city will go hostile towards you. Entering using a key or by picking the lock after hours will net the same result.
It is advised to use caution when starting fights in the marketplace, due to a Fat Man being present in Flak ' n Shrapnel's, one of the hostile non-player characters may take it and use it against you.
If the player angers the Security there by staying too long after hours, instead of turning hostile, they will turn hostile and turn friendly again. Over and over.
Despite being surrounded by objects, commanding Dogmeat to find an item will result in him instantly returning to you, and you can ask him to search again. Although the result will be the same.
Even if they are nowhere near their shops, the merchants will still say the greetings they would say if the player were to enter the shop.