It kinda depends on what you're trying to do. Finish the quest line? Farm? Just mess around and see the new content? Telling you how best to farm is... complicated, to put it mildly, but I'm pretty sure I can tell you how to survive. Here goes.
The basic stuff you need to know can be found in the wiki artcle on
Underwater Adventuring. Put briefly, the sea has a lot of penalties, and you can quite easily end up wasting hundreds of adventures if you don't realize that they exist. For instance, your breathing equipment and the "ocean pressure" penalty each lower your item-find modifier. If your total modifier drops below -100%, you you will not find items. Ever. The wiki article explains in more detail.
Information about the specifics of the quest line can be found at the following links:
Old Guy quest,
Sea Monkee quest. I have run through as much of the quest as has been released so far, and with a Level 17 Turtle Tamer I did not experience any serious problems. It took me 78 adventures to complete the quests through to where you find Grandma, 39 actual adventures + 39 adventures from the "it's hard to move underwater" penalty.
GearThe monsters are similarly dangerous to those in Hobopolis, and most of the same equipment you would use there is useful in the Sea as well. This means Mr. Store items, ascension rewards, hobopolis rewards. There is also some pretty decent gear that drops in The Sea, which you can either farm or find in the mall. Elemental resistance is much less useful than it is in Hobopolis, but your normal Hat and Pants defenses are effective, so damage should be fairly manageable. There are, however, a lot of monsters in The Sea who poison you during fights, so it's a good idea to carry some
anti-anti-antidotes with you at all times.
Food If you're exploring the sea for fun just eat normal food. I don't think there is any point in using the special Sea food unless you're going to be farming. In which case you'd probably be eating
sushi, which requires a pretty major investment to get set up.
FamiliarsIf you're not farming, using one of the underwater familiars could be fun. Otherwise, just use the ordinary farming familiars with their breathing equipment. None of the water-breathing familiars offer useful farming effects.