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The basic mechanics for all of these romantic relationships, despite the vastly different dialogue which plays over them, are exactly the same. All Shepard needs to do to impress his or her would-be lover is to talk to them aboard the Normandy. You'll always have this option when you're not on a planet, and in fact the option to talk exists with every character in the game and usually shows up on the dialogue wheel as something like "Do you have time to talk?"
With romantic interests, however, a larger number of dialogue options will begin to unfold over time. The results of these options are, to be frank, very obvious. For example, Miranda will talk about how her body was genetically manipulated to be perfect, leaving Shepard open to some obvious pick-up lines. As in the rest of the game, the Paragon or "good" options are located at the top of the dialogue wheel while the Renegade or "bad" options are located at the bottom. In most cases picking the bottom options will cause Shepard to same something offensive, and there is sometimes a middle options on the dialogue wheel which simply allows Shepard to opt out.
Eventually the dialogue with a romantic interest will reach a sort of road-block, at which point the romantic interest will say that they need time or are waiting for the right moment. If you try to go further you'll reach a dead-end of dialogue options where both Shepard and the NPC repeat themselves. Once a romance has reached this point, it can go no further until Shepard commands the ship to enter the Omega 4 relay. This is what triggers the final scene of the romance.