Syndicating in Warband means corrupting groups of nobles for your interest. This can have many benefits, such as messing up the kingdom's unity, convincing lords to join your side and turn against their king, or forcing someone to be rejected and exiled from the kingdom, meaning that he joins another. But it can be problematic if the lords who joined you have rivalries, and you must do your best to prevent it and keep your subjects loyal to you.
In order to obtain a Syndicate Lord, you must gain their favor (most often through completing tasks for them), and subsequently causing them to doubt their current liege. This is quite difficult without a high Charisma and Persuasion level. A high Right to rule helps, as does being a kind and just king, for example rewarding Vassals for their efforts, protecting and strengthening villages/castles/towns, and refraining from needlessly provoking enemies. Most importantly it takes time, most lords require large amounts of work in order to be turned traitor, so just pick a handful of lords you would like to have and work at sowing the seeds of corruption.
An excellent way to do this is to never take lords you have captured prisoner. You gain several relationship points each time you free one, although certain lords will take freedom as an insult and you will lose relation the next time you meet up with them.
A final, and sometimes dramatic, benefit to this technique is when a lord comes over to your side he brings all his properties with him. If you have chosen well and he controls castles and towns this can include a sizable portion of an enemy faction's holdings.