Now that you're aboard the Nexus, it's time to learn and explore. In general (in Bioware games, at least), you'll want to examine everything, talk to everybody, and exhaust all possible dialogue options. Even if you already know the answer to a question (or just don't care), there may be XP linked to the discovery. You can, mercifully, use the Space bar to skip individual lines of dialogue without exiting the conversation entirely.
You can practice this on Addison, on the top tier of Colonial Affairs. She doesn't like you much but she has some good info to share.
Even more text heavy is the good Director Tann, in his office downstairs.
Leaving Tann's office you'll have chance to observe an exploding panel, which is the hook for the Station Sabotage side mission.
On the opposite side of Colonial Affairs from Tann's office, is Kesh's. Chat with the krogan for little more local lore, and a hint of mystery.
Exit Colonial Affairs east, to a large hall housing Operations, which is stuffed with possibilities. In the Militia Office you can- Get acquainted with Kandros, the Turian militia leader, and use the Death-Star-looking console next to him to get access to Strike Team missions (a little ME3:Omega Easter Egg for you- Kandros is apparently Nyreen's cousin).
You can start the First Murderer task by talking to the green faced turian by the desk.
And you can catch up with Liam. Across the hall are some crates that hide a lootable container, a jail that you'll have to visit for a side mission, and an Arms Merchant.
Having a gunshop actually inside a jail seems weird, but you should still take the chance to empty your pockets of all the vendor loot (or 'salvage') you've picked up so far.
At the end of the hall (east, opposite end from Colonial Affairs) is your Science Team.
Talk to all of them at length. Dr Aridana will give you the Missing Scientists task. Talk to them again and each will give your their own collecting quest- Chief Lucan has the Hitting Rocks for Science task (scanning minerals), Aridana gives Model of the Spheres (scanning planets), and Herik gives Comparatively Alien (scan Andromeda wildlife). The program required for each can be downloaded from the nearby console.
Once you've done all you want here (and don't worry, you'll come back many times), head downstairs to catch the tram. Cora's here, and will give you some affirmation, while reminding you to check in on your sibling.
Head to the Habitat section to continue your main objective- meeting up with SAM. The SAM Node is on the west side of the western corridor in this section.
SAM will open up about its true nature, and the nature of your Pathfinder enhancements. This unlocks your ability to choose Profiles- like the classes of earlier Mass Effect games, except that you can switch between different profiles on the fly.
At this point you can only activate the profile that matches up with the Training you chose during character creation, but as you continue to level up and acquire enhancements, the Profiles will become more useful. SAM will also become more useful as you level up, the block in her memory slowly eroding. Start this process by going back to the main atrium and chatting with Captain Dunn at the south end of the hall.
She'll grant you access to your Dad's quarters, which at the end of the same corridor as the SAM Node.
Explore and examine the room to check out Alec Ryder's mementos, but take special note of the weird glowing orb by the coffee machine.
This is a Memory Trigger, and is the first step in unblocking SAM's memory array. Also check out the Archive. You can read some (but not all) of Alec's logs, and a through exploration will also load some remarks from a Dr. Liara Tsoni onto each of the datapads scattered throughout the room.
Rich with knowledge, head back to the tram and to the Cryo Bay.
Immediately to your left upon entering the medical area is one Nigel McCoy. Speak with him to start the Lost Brother task.
Most of your Pathfinder team is here as well, and most have reasons for why they're not going to be on your team anymore. Which is fine- just frees up more spots for random desperadoes. You can also check in on your sibling. I wonder who put his hands like that?
You can re-explore the area if you like, but there's no new info or loot. When you're ready, head back to the tram stop and make for the docking bay.