Camping on the river is a great experience and can range from a short overnight to several nights depending on the river and the camping available. I have mostly experienced single nighters, but plan to take on longer several-night river trips in the near future.
Find a river with campsite options that suits your desired paddling experience
How many nights?
How long are you planning to paddle in a day?
Does this section of river have rapids or other hazards?
Are you looking for campsites off the water or campgrounds?
Will campsites be labeled and visible from the water?
How will you track how far you've gone?
Will you have cell service at all?
There are the obvious items of all your usual paddling equipment (watercraft, paddle, PFD, etc.) and your camping gear (tent, sleeping bag, food, etc.) but you also need space to store everything while paddling so keep to the essentials. Also consider:
Dry bags for storing all your stuff while paddling, especially if you'll be facing rapids at times
How you'll be storing & preparing your food and restocking on water
Whether you'll need to bring a loo (portable toilet) with you
Besides having more gear and longer shuttles from put ins to take outs, logistics for multi-day river trips aren't too different than a day river trip. That is if you aren't going solo and have two vehicles. If going solo consider:
Your options for a shuttle (Hike, Bike, or Borrow a ride?)
Getting a packraft (They're designed to be extra lightweight & compact)
Even with a packraft, it helps to pack as light as possible and have a backpack that comfortably holds & distributes weight