Aristocrats would apparently use soft twigs with polishing powders applied to it and use them like toothbrushes. Or, more likely, get their slaves to do it for them.

Apparently there were also weird concoctions mixed up to be used as toothpaste. Although the poorer people might have simply used their finger as a toothbrush, I suspect.

Also, urine was used as a mouthwash. Urine decomposes down to ammonia, which is a good cleaning product, so various Roman authors attest to that technique.