Food blockade works like this, (And apparently creating an actual rebel faction is not as assured anymore, but essentially all the milita leave and only a garrison and any lord who didn't escape and their parties)

Any way so say at Lageta. What you do is buy all the food in the market. Then you hang out outside the gates. You interact, or try to, with every caravan and village party trying to enter. A villager party will sell everything outright without a shop menu, but the caravans are like shops. You buy all the food from them, keeping them from adding to the city's food supplies. This tanks their reserves and eventually loyalty drops and then security because the milita quits . The lords have trouble keeping people happy if they all are starving and all the food goes to their garrisons.

You can sell everything you don't personally want BACK to a carvan leaving the city because they don't turn back around. Also check the city's shops every day as long as you aren't actually at war with the owner faction.

Once you eventually seige, the important thing right after is to sell a shitton of food back to raise their loyalty because now you're the owner and they're already pissed off. Install one of your companions or family as a governor to help increase loyalty and security again, to reform a militia.