To activate your flight plan you need to know in which FIR/UIR you're in and your callsign. You can easily get those information right after you filled your flight plan.
Next you need to go on the HQ website and see on the left column the Web UI logo.
Since your connected on the network you will be able to click on those buttons. Step 1 to get your squawk code would be to click on the ATC button.
Step 2 would be to click on LOGON/STATUS:
Step 3 to enter your FIR/UIR your currently departing from and your callsign under it.
Once done you can click send at the bottom. After a few seconds you should receive a new message like this. This mean that your flight plan is now link to your aircraft.
But it's not over, on step 4 you need to go back on the ATC page and click on Clearance Request:
On that page all you have to do is click on the small box and click send.
After a few seconds you should receive a second new message this one containing your squawk code that you would need to set prior to push back.
It's very important! That you click on this message and acknowledge your squawk code. Failed to do so can result on your flight plan not being track while flying.
After this you're all set! Your flight plan will activate once airborne and you can track your status on the Live Map.