After you complete the Geth Dreadnought mission, you will have more conversations available to you on the Normandy. You can also visit the Citadel to see a number of unique conversations with your party members, and pick up a few new side missions.
First, speak with Admiral Raan in the War Room. She will admit that, upon further investigation, it seems that the Geth VI’s (or Legions, if he lived through Mass Effect 2) actions on the Dreadnought saved you and your party, and by association, the entire quarian fleet. She still doesn’t trust it completely, as the quarians long feud against the synthetic geth will refuse her that. But she will agree that, perhaps, you shouldn’t dismantle the VI for parts. That’s a start.
Head over to the video console after speaking with Admiral Raan to decode a transmission. You will receive a video message from Admiral Anderson after you do this. Here, you can ask about how things are going on Earth, and what to expect when you have to battle Kai-Leng. You will gain a few reputation points. You may also speak with the Geth VI to learn more about the mission that it asked you to take on.
After seeing these conversations, head to the Citadel. Search the area for new missions and arguing people. Whenever you take a side in one of the arguments, you will gain either Paragon or Renegade points and a new war asset to take into battle. One of these arguments will be held by Tali, if she lived, by the C-Sec office.
You can find Liara at the Presidium Commons, on the lower level by the shops. Speak with her. IF you are pursuing a romance with her, this conversation is basically a necessity. You can ask her to be more than friends with you if you have never romanced her before. But, if you romanced her in the first Mass Effect as well, you can ask her to resume your relationship where you left off last.
You will also be able to find Kaiden or Ashley in the Presidium, provided they lived through your decision earlier and joined your crew. Sit down with him/her by the shops to have a friendly conversation. This won’t yield any romancing points, not yet, but it’s still beneficial if you want to build a rapport with him/her. After this, head down to Purgatory to find EDI and Joker. They will have finally begun dating, and you can speak with them to see how it’s been going.
After you speak with Liara, EDI, and Kaiden/Ashley, you can find a surprising third person to speak with by visiting the Spectre message terminal. If Miranda lived through Mass Effect 2, you will find a message from her. She will give you more information on her family. She says that her father is working with Cerberus, and that the two are working to kill her. After this, check your email for information on a meeting place. She will be in one of the apartments in the Presidium Commons. Miranda will ask you for Alliance resources to stop the troops that are hunting her and protect her sister. She will share more information about her involvement in the Lazarous project, then you will have to choose whether or not to give her the resources. Either hand them over for Paragon points, or claim that Earth needs all of the Alliance resources they can get to stop the Reapers to get Renegade points.
After this, you can freely head back to the Normandy and take on the next missions.