When you’re done messing around with Strike Team Missions make your way east from Kandros to find Liam, who you can chit-chat with… but he’s got little of importance to say. Ignore the Turian named Mariette - she has a quest you’ll pick up later - and leave the room Liam is in and make your way west to find a door between the two ramps to the west, which ultimately leads to the tram. Near the door to the tram you’ll find Cora, if you care to indulge in more inconsequential chatter with your allies.
Enter the tram and not the screen has a few circles indicating places you can travel to. It’s not the most elegant selection system in gaming, but align your character so the "Habitation Deck" level is highlighted and travel there. Once you’re back on the Hyperion - Operations deck head east and go down two flights of stairs then turn south and go through a doorway. Continue south through a lab, then go up some stairs to reach the atrium, at which turn west to reach a hallway, at the northern end of which is the door to your dad’s room.
As a guard informs you, you’re the sole individual allowed into the room, and it’d be a shame to let your father’s secrets die with him, wouldn’t it? First, however, go through a doorway to the west to reach the SAM Node chamber, at the end of which is a SAM terminal. Interact with it and SAM will explain the details of your symbiosis, and of the AI’s true capabilities. As far a gameplay goes, this leads to the introduction of "Profiles".
Essentially, you’ll unlock different Profiles (which largely correspond to old classes in the previous Mass Effect games) as you invest skill points into various trees. For example, focusing in Combat skills will give you access to the Soldier Profile, spending skill points in Biotics will give you access to the Adept Profile, while spending skill points in both trees unlocks the Vanguard Profile - the more skill points you have invested, the higher the Profile rank you’ll be able to utilize. Profiles give a variety of passive bonuses broadly related to the trees you’ve invested in.
Assuming you’ve spent any skill points at all, you likely have access to at least one Profile, so equip it now and talk to SAM again, who has quite a lot to say. Also note that the quest "Ryder Family Secrets" has begun. Ominous.
Ryder Family Secrets (Part 1)
Leave the SAM Node room and head down the hallway to your dad’s room. Head on inside and note the numerous things you can examine, from some sidearms on the eastern wall, above his bed you’ll find the SSV Normandy SR-2 model, which you can use to decorate your own ship, should that event ever come to fruition. Some books to the south of the gun case await commentary, as does a Coffee Machine on the other side of the bookshelf… all of this is trivial stuff, though.
Search a glowing "Memory Trigger" and listen to SAM chatter some more. Once done, head over to your father’s desk and activate the "Archive System" to access dad’s personal logs, then listen to everything in the "General Logs". To finish up in here, listen to the Audio Excerpt on the desk, listen to a second one on a coffee table, then log a third one on the bookshelf, near the books you examined earlier. Next, leave your dad’s room and return to SAM Node and interact with the SAM terminal to witness the memory you collected earlier. Finally, you can return to your dad’s room one more time and peruse his "Archive System" to find that "Encrypted Log #1" has now been replaced with the option to listen to "Ellen’s Disease". After this, the quest "Ryder Family Secrets" will go dormant again for a while.
Exploring the Tempest - Pre-launch
Time to get back to business, which involves temporarily leaving the Nexus. Don’t worry, you’ll be back soon enough. Return to the Atrium and make your way south to find some stairs. North of these stairs you’ll find a woman name Lani you can talk to, while atop the stairs you’ll find Captain Dunn, who no longer has much of a ship to command, now that the Hyperion is an over-glorified battery.
Chat with whomever you wish, then return to the tram and select the "Docking Bay" option, where you’ll finally get a glimpse of your trusty chariot, the ship that’ll carry you through the Heleus Cluster and pave a path for humanity in the Andromeda galaxy - the Tempest. Near the Tempest you’ll encounter a smooth-talking Turian named Vetra, who will use her silver tongue to bypass some nasty bureaucratic red tape and get you out of the Nexus.
After some more chatter on Vetra’s behalf and a quick walk-through of the Tempest you’ll be left to you own devices, ostensibly providing a fine opportunity to explore the Tempest at your leisure. There’s plenty to see and do in the Tempest… yes, that means more chatter, quite a lot of it, in fact. It’ll take two trips around the ship to truly see everything, so lets get to it.
The area Vetra left you in is along the southern end of the ship, the Meeting Room. There’s little to see here right now, as the Vidcon terminal - the sole object of interest in this room - has nothing for you right now. Instead head down a ramp to the second deck, more specifically the Research Room. Talk to Liam and he’ll make some throwaway remarks about research and development, after which you’ll get a starting fund of resources: Omni-Gel Canister x20, Element Zero x10, Lithium x40, Fluorite x40, Cadmium x40, Iron x80.
Now that you have some resources, turn your attention to the table nearby, where you’ll find three terminals - a Strike Team Mission terminal, a Buy/Sell Kiosk, and, of course, the Research Center terminal. The Research Center terminal is where you can spend all those Research Data points you accumulate through scanning and Strike Team Missions. Use these Research Data points to unlock various weapons, armor and augmentations. Once you research these items, you can then switch over to development and, if you have the right resources, you can create them and put them to use.
Much of the rest of the ship as of right now isn’t worth spending too much time on, as your crew aren’t in their common positions, nor are they very talkative, both of which will change shortly. In the meantime head north across a bridge to reach the door to the… well, bridge. Ignore the door for now, climb down a ladder and go through a door to the north to reach your rather swanky quarters. It pays to be the Pathfinder, no?
Turn west and you’ll find a Wardrobe terminal, which you can use to change your casual outfit and customize the color of your hardsuit. On the eastern side of the room you’ll find a SAM terminal (SAM isn’t terribly chatting at the moment), an Email Terminal (check here for various bits of text correspondence) and, depending on which version of the game you purchased, a Space Delivery Cache, with which you can claim your DLC bonuses. Speaking of which, check your Email Terminal to find the "Pyjak" email (again depending on what version of the game you bought). Finally, read the "Interview" email - which everybody should have - to start the quest "Task - Path of a Hero".
Leave the Pathfinder’s Quarters and climb a ladder outside the door to return to Deck 2, then go through the door to the north to reach the Bridge. Once inside you’ll be pestered by Kallo, after which the rest of the crew will show up . Record a saying for posterity - or not - and the Tempest will finally take off.
Exploring the Tempest - Post-launch
Freedom! Sweet, sweet freedom! Actually, scratch that, there’s more to do on the Tempest. From the Galaxy Map screen merely press [Triangle]/[Y] to return to the interior of your ship, where your crew will have settled in… and coincidentally become more talkative. Now is a fine time to properly run through the rest of the ship and chat with everybody… and perhaps sow the seeds of future possible romances by flirting a bit.
First up, talk to Suvi and Kallo on the Bridge, then head south to - but not through - the door to the Bridge. If you turn east you’ll find and empty room, waiting a future inhabitant, while if you turn west you’ll find a Loadout Station, where you can… well, change your loadout. Change your arms and armor as you wish, but keep an eye on your Weight, as more/heavier gear will result in you suffering power recharge penalties, which is less than ideal for biotics and tech-users.
Leave the Bridge and continue south across the… bridge… to reach the Research Room. While this area (and the Meeting Room above it) have nothing new to see, you can turn your attention to the Bio Lab to the northwest, inside of which you’ll find Cora throwing a bit of a biotic tantrum, which is basically an excuse to tell you about her past.
Return to the door leading to the Bridge and climb down a ladder to reach Deck 3. To the north, of course, are the Pathfinder’s Quarters, where you can now access the SAM terminal and chat with SAM some more. It’s a rather chatty AI, eh? Exhaust the AI’s dialogue options once again and leave your quarters, then head down the hallway to the south until you reach the door leading to the Cargo Bay.
West of this door you’ll find the Crew Quarters, which has little of interest inside it as of now. To the east, however, you’ll find the Medbay, where Lexi T’Perro - the onboard doctor - awaits. After a bit of malpractice she’ll start begging for Kett corpses, which… is rather worrisome, to say the least. Chat her up, then search the skeleton hologram on the northern wall, which happens to double as a Respec Station. Cough up some Credits and you can refund the skill points for one character, just be wary, however, as the cost increases every time you respec (20 Credits for the first respec then 500 additional credits every time thereafter). At this point in time, it’s not likely you’ve managed to mess up your character enough to bother respec’ing, but if you ever wanted to try out a new playstyle or go for some trophies/achievements… well, a bit of Credits and save/loading will go a long way.
Return to - and go through - the door to the Cargo Bay, then make your way to the southern end of the Cargo Bay, where two more doors beckon. Through the door to the southeast you’ll find the Armory, in which Vetra currently dwells. Chat her up, then go through the door to the southwest to reach the Storage room, where Liam is busy shuffling around questionably stained furniture. Sit down, have a drink, and chat with Liam about his past… then consider taking a long, scalding shower.
Between the two doors is a lift, which will take you to Deck 2. Ride up and go through one of the doors to the south to reach Engineering, where Gil supervises the drive core. Scan the ODSY Drive Core for a codex entry, then talk to Gil if you wish. Once done, you’ll have chatted up every crew member currently worth talking to, and have explored every part of the ship worth exploring. The Priority Ops "A Better Beginning" draws you to Eos, but first, there are two quests worth knocking out - one in the Pytheas system, and another on the Nexus.