To speak to characters, approach them and press [ E ]. Most will open the dialogue wheel conversation interface; some will simple respond with a comment.
To select Shepard's responses, move the mouse over the option that best suits your personality and click the [ Left Mouse Button]. Friendly or diplomatic options are placed on the top "spokes" of the conversation wheel, while angry or rude options are placed on the bottom. The spoke directly to the right is the default response that is not particularly friendly or hostile. You will never miss any content by choosing the default options, allowing you to safely skim through a conversation.
The spoke directly to the left is used for "investigate" options. Investigate options provide additional background, but are never required to advance the plot. If there are many investigation options, choosing the "investigate" spoke opens a sub-menu of questions. To return to the main topic select the "Return" option on the right-hand spoke.
Only Shepard may gain the persuasion Talents of Charm and Intimidate. When persuasion skills are used in conversations, they are placed on the left-hand side of the conversation wheel, and distinguished by color. Charm options appear blue, and Intimidate options red. If you lack the level of Talent required to access a persuasive option, it will be greyed out and un-selectable.
Your squad members have their own opinions on the sights of the galaxy. If you hear them make "thoughtful" noises as you walk through an area, try talking to them.