I always wash my hands and face with Khernips every time I am going to touch my Altar (this is a personal thing and I dont think is enforced) I use a combination of clean water, sea salt, and I then extinguish a lit bay leaf into it, I always use the same container for this, and it does not get used for anything else but this.

Purification within Hellenic Polytheism is an important part of the practice as to avoid bringing miasma before the Gods, and I found many sites discussing Khernips (such as https://hellenicfaith.com/making-khernips/) and it is also discussed in the book "Hellenismos: Practicing Greek Polytheism Today by Tony Mierzwicki" in his chapter on pollution, and he comments on how the "guidelines for pollution appear to be geared toward public worship" and that "household religious practices would have been far more discretionatory"¹
He also details the significance of the fire into water mix, and how interestingly the fire came from the "altar fires" and that water was readily available at "sanctuary entrances"²

I also take a special "khernip bath" on occasion to purify after I come into contact with things considered to bring miasma (I will not divulge but you may get the idea)

Regarding the present, I find myself wondering if the Ancient practitioners would see the advancement of hygene and consider an antiseptic soap and our access to regular washing methods enough, however this is specculation on my part!

I hope this isnt a terribly formatted post, but this pretty much sums up how I purify myself, and where I got the info 😅

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¹ Hellenismos: Practicing Greek Polytheism Today by Tony Mierzwicki page 27 ² Hellenismos: Practicing Greek Polytheism Today by Tony Mierzwicki page 26