What is the cleansing process for becoming clean after becoming unclean through a dead body in a tent, open field, grave, etc., and what part of this can we do today?
Answer From The Annual Reading Schedule - Week 36 Notes For Numbers: The cleansing process is mentioned in Numbers 19:17-20. The part we can do today is this: If we go to a funeral (inside where a dead body is) or a cemetery (possibly walking on graves), although we don't have physical red heifer ashes and other things needed, we can wash our garments and bathe in water on the seventh day as mentioned in Numbers 19:19 to demonstrate our desire to be obedient to His word. However, in doing this, we have to realize this is not really completing what is required in the law since we do not have the red heifer ashes and other things required. This does not accomplish what is required in Numbers 19, but rather is being suggested just as a means to show Yahweh we do love Him and care about what He says in His Torah (law/teaching).
Not being able to accomplish this literally as Numbers 19 requires seems to be another reason that we also cannot do a literal Passover as commanded in Exodus 12. For the other reasons why we cannot do a literal Passover as commanded in Exodus 12, read the reading notes Week 16 answer for the question, 'Should believers today take a lamb on Passover and perform the Passover with all its' laws and ordinances, including the blood on the doorposts, etc., or not?'.
However, what does accomplish all that we need to be pleasing in the sight of Yahweh is the offering of His Son Yahushua who was given for us, to make atonement for us and to cleanse us from all unrighteousness (Isaiah 53, 1 John 1:9).