n order to romance a companion, you need to get them to the highest level of companion relationship status (they idolise you) and then engage in a dialogue, selecting the “romance” dialogue option and successfully passing a Persuasion attempt. Higher Charisma and Luck are a help, but you have a chance regardless.
Every companion and love interest has several levels of potential friendship with you, starting at neutral. Relationship status can dip into negative, and if you piss someone off enough they won’t travel with you any more.
Your relationship level with each companion changes depending on your character’s behaviour while in a particular companion’s view. You don’t need to be travelling with the companion for this to take effect; if your friends are all standing around Sanctuary Hills waiting for you, for example, they may alter their opinion on you based on what you do while you’re there.
If you’ve got multiple people around you at a Workshop, or working with you as happens during some missions if you bring a companion, they will each react individually to your choices.
If you wish to increase your relationship level with a companion or love interest, you should travel with them whenever possible, in order to maximise the opportunities for them to observe your behaviour. If you need to do something they won’t like, you should send them away. Their “field of view” is pretty small, so you can also command them to stay in place at a distance, but be aware that they’ll sometimes see you through walls. Be sure to quicksave if you’re uncertain.
Every time your relationship status with a love interest or general companion increases, you’ll get a message on screen (“Piper tolerates you”) and they’ll want to have a chat with you, allowing you to get to know them better. You’ll know if they have something on their mind because they’ll keep saying the same thing over and over again; face them and stand close to bring up the conversational prompts.
As your relationship increases, you may be given the option to flirt during these little chats. You need decent Charisma and Luck to pull this off successfully, but there are no negative repercussions for trying until you reach the final check.
If you want to know how things are going, open the Command menu (stand close to and face your companion, and press Cross/A) and select Talk. You can then select Relationship; the resulting dialogue changes as you grow closer, and in the early stages (neutral, tolerates) can offer clues on what sort of behaviour your companion is attracted to.
When you hit the highest rank of companion relationship (“idolises”) you’ll get one more dialogue before you unlock the companion’s ultimate perk. You should quicksave (or better, make a manual save) here so you can try your luck with the romance persuasion attempt multiple times.
If you’re successful, well done! You’re in a Fallout 4 relationship. When you sleep while your romantic partner is near, you’ll earn the Lover’s Embrace bonus, which grants a 15% XP boost for a limited time.