There were conflict zones in Jera but they dissapeared a few days ago. I believe that the news on the Galnet board is saying that they may reopen soon. Not sure if we have to show an interest in the system by running missions for the Nationalists or something to get the civil war going again or maybe after the Durius campaign has finished.
In Durius there are a number of Conflict zones. You will need to fly towards the stations, which are 280,00ls away. When you are within 1,000ls of these you will start to see Conflict Zones appear in the navigation panel. They are labelled High or Low conflict zones. Simply fly up to them and enter them as you would any USS.
Once at a conflict zone, before fighting, remember to select your faction from the Functions Tab on the right hand UI panel.
All combat bonds must be turned in at one of the local stations. It doesn't matter who your fought for, both sides get turned in at these stations.
Hope this is helpful. And hope to see you in Durius, hopefully on the same side.