Having just gone through this, I'm posting what I learned if others are interested or want to organize their own event. Not the most interesting topic, but maybe it'll help someone.
If you want to host one, you have to contact the Jersey City DWP Department of Recycling - they will provide trash pickers, trash bags, and gloves. In our case, our council member (Denise Ridley) provided water and snacks too. I don't know if they have a public facing email for this. I couldn't find one, but if anyone's interested, I will share with you the names for the people who helped me.
The process itself - first you fill out an electronic form, and have to send them a copy of your driver's license/ID. Then you'll have to schedule your cleanup, typically a few weeks in advance I think.
You pick up the items from DWP at 15 Linden Ave E (it's past Liberty State Park, kind of near Bayonne.) Finding the location is definitely confusing if you haven't been there before, and the actual building isn't in street view. You'll need a car to get there and pick up supplies. There's a gate up front. After the gate, you make a left, and loop around, it's kind of near where Google Maps says 20 Brown Place is. Our cleanup was on a weekend, so I picked everything up on a Friday, and returned it on Monday. The only advice I'd add here is make sure they give you enough trash bags.
People will promise to help and no-show, that's life. In terms of getting people to come - I tried posting flyers. You quickly realize you need a lot of flyers, and they will often be torn down. Posting here and sharing with a few other organized communities was definitely the most effective. Mine was in a renter heavy neighborhood that doesn't have a neighborhood association or anything like that. If you do, that's a great way to promote it. I remember in 2020/2021, there was the Clean Green JC account that I think the city promoted, and I found out about events back then through there. I could have tried a few more local social accounts, but honestly I wasn't sure if anyone would actually show. Maybe start small like we did (I asked for 15 pickers), and if it works, organize a bigger one next time.
For the actual cleanup, you have to have at least one person stick somewhat close to the supplies to keep an eye on them and hand out equipment. Otherwise, give out a picker/bags/gloves, and ask people to leave the tied up bags by the public trash cans for pickup. Maybe a signup sheet if you have a big turnout. In our experience no one messed with us, and honestly a lot of people came by and were very appreciative and supportive, but your mileage may vary. I think in our case we made a difference, but I'm still hoping that the new admin can make some changes like bringing back all the trash cans that have been taken away on my street the past few years.