V has 4 options for their main romance throughout the game, with additional encounters possible with other characters; these additional encounters do not mean anything for the progress of the game and are simply there as "side-flings".
The current options are:
Judy Alvarez Romance
How to Romance Judy
After completing this quest, the romance is fairly easy to advance. All you need to do is do her quests, keep in contact with her, and ensure that you always ask her opinion on what to do when prompted. Follow whatever she says and, eventually, you will end up with the quest Pyramid Song, where Judy takes you diving.
This is the marker for the start of the romance and is the first time when you can truly ruin your chances with Judy. Show interest in the mission and, when prompted, "Touch" her. This will begin the romance, but there is still 1 chance to ruin it: the next morning, when asked about the previous night, tell her that it was the start of something amazing.
This will solidify the relationship with Judy and unlock the possibility for endings with her. This will also unlock her apartment for V to use.
Getting a Good Ending with Judy
In order to get a good ending with Judy, you have to complete all of Panam's sidequests, so that she accompanies you into Arasaka Tower. When confronted with the choice, choose to go back into your body, rather than letting Johnny take it over, and you will end up with the best possible ending with Judy.
Panam Palmer Romance
Romance with Panam
The romance with Panam is extremely easy to forge, similar to that of Judy Alvarez, as you essentially just have to support Panam in everything she chooses to do.
During the Ghost Town mission, make sure to ask if she wants to share a room with you at the motel. When she agrees, saying that every room has 2 beds, tell her that was not what you had in mind.
Continue her questline until you reach Life During Wartime, where you will need to ask Panam to come and help you find Anders Hellman. After you have completed this task, you will have to face Saul with her. Stand up for Panam - she will thank you if done correctly.
Continue through her questline, always staying at her side when you can, both physically and in conversations. Always side with her when she speaks to Saul, supporting her.
When Panam puts her legs on your lap during Riders on the Storm, tell her to take her shoes off and relax, then touch her thigh.
During With a Little Help From My Friends, always agree with Panam and eventually touch her hand when prompted. Make sure that when Saul messages you, you hide the plan from Saul by telling him you have no idea where Panam is. The final prompt during this quest is to "scooch closer" to Panam when sitting around the fire with the Nomads.
The final quest where V has a chance to develop the relationship with Panam is Queen of the Highway; it is also the mission where you have the sex scene with Panam. When you are inside the Basilisk with her, let her touch you, which initiates the cutscene. You will be interrupted, but at the end of the mission, you will then be able to kiss Panam, which completes the romance with her.