The basic pattern of play is to find a unit in a map or list window, click once to select it, and then pick commands from the "Play" menu. There is also an "auto-select" mode that does the selection for you and interprets mouse clicks as movement commands; Xconq actually starts up in this mode.
You can select units by clicking on a unit, shift-clicking a group, dragging out a selection rectangle, or by using Command-A to select all units. A selected unit is indicated by an outline box - solid black to indicate that it can move, dark gray to indicate that it cannot move, and gray to indicate that it cannot do anything at all (at least during this turn; some types of units may only get to do something once in a while). If clicking on a unit image doesn't have any effect, then it's not a unit that belongs to you.
To move a selected unit, drag the selected unit to its desired new location. The unit might not move right away if it doesn't have the action points, but it may get some in the next turn. To move all selected units, do Command-click on the desired location and all of them will attempt to move there.
To shoot at another unit, you can position the mouse over the desired target, type 'f', and all selected units will attempt to fire. This works even if all units are selected, so you can call down considerable destruction with 'f'! If the target is too far away, nothing will happen.
To find out more about a unit, pick "Closeup" from the "Play" menu or do Command-I. This brings up a window that shows all kind of data about a single unit. You can leave this window up and it will always be kept up-to-date.
To jump ahead to the next turn, do the menu command "End Turn" or <return>. You may have to do this if some of your units still have action points, but not enough to do any of the things you want them to do.
The Game window (Command-1) shows the status of all the sides in the game. The window shows both the emblem (if available) and name of each side. A small computer icon indicates that an AI is running the side, while a face icon indicates your side's relationship with the side (smiling means friend/ally, frowning means enemy, flat expression means neutral).
Each side also has a progress bar that shows how many actions its units have left to do.