There are three main locations where you go to have your characters perform actions: the occupants pane, the tab list (at the top, below the character box), and in several shutter panes, in the center, below the main description pane.
Action tabs and panes are often situational and will appear or disappear as the actions they contain become available. For example, the "alchemy" tab will only appear when the character is in a location that supports the use of the Alchemy skill (such as a Pharmacy).
Clicking on the tab or the pane will open it and allow access to the actions within. Just like the tabs or panes themselves, some actions will only appear when the situation warrents (for example, there will be no actions to attack barricades if there are no barricades to attack).
Other times, the actions will be disabled (greyed out). This is usually because your character does not have sufficient Action Points or Magic Points, but can also occur if you are missing a vital component (such as a toolkit).