I can speak for Islamic and pre-Islamic Arabia.

Early islamic tradition emphasizes heavily the practice of using the roots of the native Salvadora Persica tree for oral hygiene. The practice was so common that this specific tree is also know as toothbrush tree, and islamic tradition stops short from mandating that the roots are used prior to every prayer.

Even today sticks made from Salvadora Persica, known as miswak, are popular for oral hygiene in the Arabian Peninsula, India, and generally in the Muslim world. The practice can be found in non-islamic regions to which Salvadora Persica is native, as well as islamic regions where the tree is not native to.

Traditionally, the sticks would be harvested from the tree's roots and twigs then used in their fresh state. The outer bark of the roots is first chewed to form bristles of the inner part of the stick. The bark itself has its own pleasant smell which works like a mouthwash, then the bristled stick is used like a brush. There are entire Wiki-How articles about proper usage of a miswak, so I will not get into the details. Records of trading on the Incense Tradin Route shows that dried Miswaks were commonly sold there as well. A buyer would need to soak a miswak in water before they use it.

Tracing the daily usages of miswaks in islamic arabia one can see a similar pattern to how toothbrushes are used nowadays. Specifically, the prophet of Islam Mohammed was quoted to have practiced and encouraged oral hygiene right after waking up, before social gatherings (to pray), and even before love-making. Moreover, the texts available specificy using miswak to clean your gums, tongue, teeth, and for flossing. Islamic teachings also specifically prescribe miswak as an antidote to both plaque and yellow teeth.

Those islamic quotes are understood to be encouraging of practices that pre-date Islam, as apposed to setting a new trend. The practice of using miswak survives to this day, although it took a more religious tone with the wide availability of other methods of oral hygiene. One would commonly find people selling miswaks right at the doors of mosques in modern-day Arabian Peninsula as well as other parts of the Islamic World albeit less commonly. Some toothpaste brands offer miswak-flavored toothpaste, and many academic studies are conducted to examine its effects. As this is outside of my field, I cannot speak to their results, and the reader is encouraged to do their own reading on that regard.

Miswak was only one method for oral hygiene used in islamic and pre islamic arabia. The leaves of Cyperus Rotundus were also chewed for their anti-odor effects as well as the leaves of Ziziphus Spina-christi. It was also common to wrap a piece of cloth around one's finger and use that as a brush when miswaks were not available. Both miswaks and pieces of cloth were sometimes dipped in a variety of powders or pastes before application, with rose water being one of them.

I will return later to expand on other practices of oral hygiene and answer questions.

Chewing on charcoal and parsley will clean your teeth as well as toothpaste (just ask my dogs - who to be fair eat less sugar than I do!). It is however, a bit gross.

Teeth brushing has been around since at least the Ancient Egyptians - with evidence as far back as 3500BC of toothbrushes and toothpaste made of rock salt, mint, and pepper. The first toothbrushes that resemble today’s, were made in China in 15th century.

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The trend of getting something abrasive to use as a toothbrush (a feather, or stick seems to be popular), mixing it with something abrasive (salt if you are fancy or by the sea, charcoal if you are less fancy), and finally something which smells nice but isn't expensive (parsley, peppermint etc) seems very old and to crop up in a lot of cultures, starting in 5000BC.

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What I can't seem to find is how often people would do this (although in Rome it was recommended by Celsus (c 25BC – c 50AD) to wash their mouths out every morning). However, it's a common misconception that ancient peoples were dirty, we seem to think that modern times have one up on hygiene but that is often not the case.

As someone else had noted (its has now been removed), a lot of the ingredients in that recipe (it had things like cloves in it) seem to be expensive, however the trend of brush + abrasive + smelly herb would be very accessible to everyone. There were some departures from this, such as in 1728, Pierre Fauchard, who is considered as a "father of modern dentistry," in his book Le Chirurgien Dentiste (The Surgical Dentist), didn’t recommend brushing of teeth but rather cleaning the teeth with a toothpick or with a sponge soaked with a mixture of water and brandy.

I have asked a somewhat related question quite a while ago and got an interesting answer from /u/Ragleur about, amongst other things, mouse dung.