As others have said, start squatting to poop and there will be much less residue (or even none at all!). Then cleaning that area is no different than anything else.

As for keeping the nether regions clean - shower toilet/washlet/bidet. Seriously brilliant devices and absolutely worth getting one. Living in Japan the world leader in toilet tech; these things are ubitiquous - toto washlet is the most common one. Awesome devices that really do a great job of washing up after you go. The latest ones are very advanced. I am so used to them now that the thought of just using toilet paper is quite disgusting.

The only time I don't use them is public toilets where I always go for the squat toilet (even if there is an option), which is by far the most natural way to go and you dont have to "touch" anything and the squat position open up the 'trajectory area' while going, so much less need to wipe. My dream combo would be a squat toilet with a washlet toilet beside it.

Washing with just water is fine, it's very "Paleo" and if you're eating and sleeping great it's all your skin needs. There are a ton of natural cleaning methods that work great, some lean towards Neolithic but they're all safe and healthy - no harmful ingredients.

Brushing

Brushing's about as caveman as it gets, dry or wet. You're scrubbing off dirt and skin cells (exfoliating) with bristles, natural or animal. Works great, just don't brush too hard and give your skin time to rest in between.

Clay

Mud masks and clays in general are 100% natural, and effective. Not so much for washing/scrubbing, but great for tightening up pores and drawing out dirt/oil in your skin (as opposed to on it). Rolling around in mud has probably been done since the dawn of time.

Oil Cleansing

Oil cleansing is great, just don't do it more than twice a week (I don't shower much more than twice a week, for that matter). Look up the OCM online, the devil's in the details but overall it's a safe, effective method. As someone said already, it's what the Romans did.

Soap

Cleaning with soap is about as old as cleaning with oil, and technically it's a form of cleaning with oil (saponified vs. in its natural state). Soap dries out my skin too much so I don't use it, but as long as it's a natural soap I don't see anything wrong with it.

After that there are a ton of foods you can use to exfoliate/scrub/clean up. Salt, Sugar, Honey, Cider Vinegar, Oats, and Yogurt come to mind. Like I said above, washing with water is all you really "need," but you can take your skin from good to great with natural methods that wouldn't have been available to a caveman.

In addition to physical means like (dry) brushing and using washcloth, you can massage honey on wet skin, then rinse it off with warm water. If you leave it in the fridge, the honey christalizes and works even better, like a gentle scrub.

Water and a washcloth for the last 9 or so months. No soap, no shampoo, no body odor, and no complaints. I feel as clean as ever.

I have very liberal approach to choosing what's primal what isn't. I don't use much soap, but I love to use once a week or so good, natural peeling mixture. I buy only hand made online, with all natural elements, where the peeling element is sugar or tiny pieces of nuts with oils and so on. After that I cover myself with coconut oil... I love the way my skin feels.

I do not have a problem with me using peeling cosmetics, b/c I am pretty sure people used to use sand or other harsh substances and objects (a bundle of leaves) to take off harsher dirt or scratch the skin to take off the old, death cells b/c the skin was itching or so.

95% of the time I am water only for body (occasional baking soda does seem to help with hair though) but I love to use a loofah sponge and another brush. Today had some extra time, scrubbed whole body with loofah, then brush, then washcloth. My skin is like silk! If you don't happen to know what a loofah is just google and some images will come up. It is made from natural vines.

As I just typed this out seeing Susan's answer so consider this a +1.

I have been without soap, shampoo, etc for over a year now. I've used wash cloths in the past, but what works for me is a skin brush. It can be used wet or dry (I prefer wet). You just gently run it over your skin. It gets rid of the dead skin cells and such leaving your skin clean and smooth. No soap needed. I've done this for a while and I've yet to have problems with odor.

As far as the other question, I second what "42" said.

Water and a Washcloth make cleaning easy. If your nethers are harder to clean... learn to squat. The idea behind squatting is that you will have a clear straight path for waste, which doesnt happen when youre doubled over sitting.

http://www.marksdailyapple.com/squat-poop/

Re the NSFW bits: cleanliness in the taint area is largely a matter of producing poops that don't need any wipe-up afterwards. Healthy dogs and cats usually have clean bums* and healthy humans shouldn't need toilet paper. Pets with crusty bungs and messy poop aren't that healthy or are being fed low-quality foods. Humans too, I guess :)

Out of habit I use TP and I also use soap -- no shampoo other than maybe twice a month -- but let's just say I haven't needed TP in ages.

*of course we all know that they can groom their own butts, but I wonder how much of that goes on in wild cats and canines.

I use one of those shower massage squirter attachment things at the end of a hose in my shower. If you have a screw on type pipe end where the shower attachment goes, you can just screw that off and screw a longer attachment instead. I got mine for about $20.00 at the store. I originally got it so I could wash my dog easier. That's generally all I use now. It will vigorously remove most unwanted stinky stuff. If there is ground in dirt like maybe on the feet, then I will typically use a scrubbing pad with water. If I am shaving, I will sometimes use some all natural 'saponified oils' soap for those areas. I also use a light application of saponified oils and then rinse on my hair to keep it silky without stripping all the natural oils. The trick with the hair is to only use a tiny bit of soap with minimal lather so as to not overstrip the hair. I tried using baking soda and other no soap products for the hair but I just had no luck. My hair felt grundgy instead of silky and it was too oily. I have very fine hair so the oil really shows. Some people have said the no soap thing on hair is not so easy if you live in a hard water area, which I do, so maybe that was part of it.

In ancient Roman baths, supposedly they would rub olive oil all over, then scrape the oil (and the dirt) off with a piece of wood or some other implement, then hop into the bath! I have not tried this personally.

Water is a good cleaner in itself. Just rubbing any area of your body while cascading water over it in the shower will get 99% of all NATURAL soil off. Usually, the result is you will just smell like a human which to other humans is no smell at all. My theory is soaps for the body were developed to wash off all the other artificial petroleum based products people put on their skin; suntan oil, make-up, etc. They are designed to stay on in a moist environment. Anyway I haven't used soap or shampoo in a long time and I don't smell (verified by my hypersensitive wife!)

For your NSFW: If the anus is closing properly that area is no different than any other. If scrubbed by hand with water it will be fine. The skin around there doesn't hold the stinky any more than other areas and fecal matter will wash right off.

Not everything that was used/invented post-Paleolithic is a bad thing. My mother in law makes all natural soaps out of animal fats and essential oils. There's nothing wrong with wanting to use soap, just because Grok may not have. He also didn't drive a car, utilize electricity, or shop at farmers markets. We have the advantage of having modern things and research and even, in some cases, modern medicine, at our fingertips. We have to use good judgement as to whether or not the things are healthy for us. All natural, homemade soaps? I see nothing wrong with that. Plus, I don't have to worry that I smell :). Just my 2 cents.

I've been washing with only water for some time now (4 months or so). I've been using a washcloth for the first time in my life (I'd always wondered what they were for) :) I've not had any issues with odor since using the cloth.

Well they probably still bathed from time to time in whatever lake, river, or beach they could find. And the lucky tribes would have found the waterfalls. Maybe sand helps clean the body?

Perhaps they created some kind of scrub from ingredients like clay, rock salt/sea salt, and perhaps even animal fat and make some kind of concoction. I'm just speculating.