The basic concept of the online debugging is to set several breakpoints or watchpoints and run a mission or campaign. When one of the breakpoints is hit, the game stops and shows the script debug screen.
Wrong side? Go back to [Script debug].
First, start the game with parameter '-d'. (When you installed the game on a windows system, there should be a Link named 'SpaceCombat Debug' in the start menu.) This starts the game in Debug mode with the debug menu.
You should see this screen.

Now click on the 'Debug' button and enter the script debug screen.

Here are some basics of the scrip debug screen described: [Script debug basics]
On the left side is the script window. You can load script files here. Simply right click the window to open the context menu and select 'Open file' (or hit CTRL+O). After loading a script file, it should be shown in the window.

You see the script file name in the header of the window. There is some high lighting of the script file:
When you move the mouse cursor over a action/condition function, the function gets a violett background color. When you now open the context menu (right click), there are some options for the selected function (e.g. set breakpoint). Active breakpoints are shown with a dark red background color of the function. The current step position is indicated by a red background color of the function.
Right click on a function to open the context menu and select 'Set breakpoint' to create a breakpoint here. (You can remove this breakpoint with the context menu too.) After setting all breakpoints, you can click on the 'Continue' button on the left lower side. Now the game continues and stops at the next breakpoint.
Right click on a function to open the context menu and select 'Set conditional breakpoint' to create a conditional breakpoint here. (You can remove this breakpoint with the context menu too.) This dialog will appear:

Here you can set several options for the breakpoint.
You may restrict the breakpoint to a special object in the mission. This is useful, when several object have the same AI script, but you want to debug only one of them. Set the checkbox and enter the objects name (exact spelling, case sensitive).
The 'Scan' button and restriction to a section is only in offline mode available.
Finally, you may also restrict the breakpoint to a defined time span. Set start and/or end time stamp. Leave the boxes empty for no limit.
You may set more than one restriction at the same time. So, you can set a breakpoint, that is restricted to a defined object AND is only active in a defined section.
After setting all breakpoints, you can click on the 'Continue' button on the left lower side. Now the game continues and stops at the next breakpoint.
The variable window is on the right side of the screen.

All known variables are shown here. When you step (by clicking on the 'Step' button on the lower right side), old values are shown in white and new values are shown in red.
When you select a variable in the variable window and right click on it to open it's context menu, you can copy it's value to the clipboard. This is useful, when you have a long string in the variable and want to copy it to a text editor. (Hint: This feature is more useful, when you run the game in window mode and not in full screen mode.)
You may also set a watchpoint in the context menu of the variable window. Watchpoints are like breakpoints (they stop the execution of the script). They work not on a function but on a variable. Open the context menu of the variable window.

In this dialog you can select the options for the watchpoint.
When you created the context menu on a variable, then the name is set in the dialog already. Otherwise you have to enter the variable name. The 'Scan' button is only available in the offline mode.
You may select several options for the watchpoint. Should it break on every change of the variable? Or should it break, when the value meets a defined condition. You may also restrict the watchpoint to a defined object. This is useful, when you have several objects with the same AI script (and therefore the same variables).
After setting all watchpoints, you can click on the 'Continue' button on the left lower side. Now the game continues and stops at the next breakpoint/watchpoint.
Now you can run a mission, load a saved game, start a campaign and so on. Select the file to run with the 'Browse scenario' button and then click the button for game/Load/Campaign...
Now, the mission runs and it will stop, when one of the breakpoints or watchpoints is hit. In this case, the script debug screen is shown and you can analyze the data.
Now the windows are filled with data.

The time slider and the log window are not used in the offline mode.
The script window shows the current step position and the variable windows shows all known variables.
You can set up more breakpoints and watchpoints or delete old ones.
Do single steps by clicking the 'Step' button on the lower right. For each click, the game moves one step to the next action/condition function.
After setting all watchpoints, you can click on the 'Continue' button on the left lower side. Now the game continues and stops at the next breakpoint/watchpoint.