You may want to look through the FAQ here. There is a nice section on Toilet Hygiene:
https://www.reddit.com/r/AskHistorians/wiki/health#wiki_toilet_hygiene
This post answers your question specifically. There are a couple of threads you can look through:
https://www.reddit.com/r/AskHistorians/comments/y8k17/when_did_toilet_paper_come_into_common_use_in/
This was asked before - specific to Roman communal toilets. The answer in that specific instance is that they used a wet sponge on a stick, so that can give you some idea as to common methods:
An interesting quote (also from that thread, by /u/Astrogator):
Seneca, Epistulae LXX, 20
For example, there was lately in a training-school for wild-beast gladiators a German, who was making ready for the morning exhibition; he withdrew in order to relieve himself, – the only thing which he was allowed to do in secret and without the presence of a guard. While so engaged, he seized the stick of wood, tipped with a sponge, which was devoted to the vilest uses, and stuffed it, just as it was, down his throat; thus he blocked up his windpipe, and choked the breath from his body. That was truly to insult death!
Pretty vivid, and this little paragraph alone has lots of interesting bits of insight into gladiators, Roman expansion and slave practices (the gladiator in question is Germanic), etc. It is interesting that he was so distraught with gladiator life that he would rather choke to death on a sponge used to wipe faeces; but the interesting point - with regards to your question - is that it is taken for granted by the author that his readers will know what he is talking about with the sponge-stick. The inference is that this was a common method used to clean after using the toilet.
Here is an artists interpretation of a communal Roman toilet.
You can see a fresh water source running through the centre to wash the sponge that the occupants are holding. This is based off of sites like this:
You can see the trough in the ground where the fresh water would have flowed. Note that the artists interpretation is incorrect however in several ways: the Romans would probably have used the toilets in a squatting position, not a sitting position, the toilets were typically constructed of stone, not wood, and the Romans would not have been wearing trousers, but a tunic flowing down to the ankles which would have offered a degree of privacy as they squatted above the toilet hole.
The slit that goes down the front of the toilet would likely have been used to pass the sponge up for cleaning while remaining in the squatting position.
Moss, lichen and old fabric are all common in the UK cess pits. They all offer a certain amount of absorbency and the natural products would be in relative abundance. At the Cooperate excavation in York dating between the 8th -11th century, all three have been identified. Fabric is much rarer and examples found are patched or threadbare indicating material that has ended it's usefulness in clothing.
In a pinch leaves could be used I suppose. We do have organics residue in cess pits that looks promising but not definite. Leaves lack the absorbency that moss or lichen provides.
Just to add a little scope, "before toilet paper" is very nearly within living memory for big swathes of humanity.
An anecdote from a book that has an utterly different purpose and intention might help -
Victor Klemperer was a German Jew who (barely) survived WW2 in Germany and kept a very detailed diary that has been published in 3 brilliant volumes.
In discussing the day-to-day privations that were getting worse in the late 1930's and WW2, he mentions rationing of personal items. Shaving cream, soap, and toilet paper were bought with cash + ration coupons for these miscellaneous non-food things. His Aryan wife got the stamps; he got fewer or none as time passed.
While complaining to his diary about how things are getting worse, he gets around to the question at hand.
Middle class Germans were accustomed to toilet paper.
This had only recently been the case. He never saw or used it until he was 40, he says. (this would be 1921.)
They typically used newspaper torn into rectangles and kept in a drawer where it would be convenient back in the day.
Going back to this older arrangement was complicated by the Nazi's also forbidding Jews to buy newspapers. His Aryan wife had access, but other Jews did not have this advantages. Also, there was some lively discussion whether he could be arrested when Nazis (regularly) inspected their home and found newspaper. Could he get away with saying it was his wife's? Nazi regulations were not customer-friendly enough to give a clear distinction.