Talk to either of your 4 romancable companions. When you talk to them be understanding to the one you want to romance and see things from their point of view and come on to them whenever you can. That of course requires you to look at the dialogue options.
For instance if you plan on romancing Morrigan there will be options when you start talking to her and asking her questions, she will ask that she does not "probe" you for information, and you can answer that she can probe you anytime or say how cute she is. If you give her any of her plot gift like the mirror or Flemeth's grimoire you can ask for a kiss and that will also initiate the romance.
With Leliana you can ask her what someone like her would be doing in the Lothering Chantry. She will ask you by what you mean by that, and you will say ask why someone so beautiful as her would be doing there. She will reply with asking if you don't think there are beautiful Sisters and that you'd be wrong if you thought so. Then you can answer that "They couldn't have been more lovely than you." to initiate the romance. If you plan on ending it, all you need to do is to be a jerk and lose lots of influence with her.