Most acceptable fast to the Lord is to help others....Isaiah 58.
But we do know that fasting is also still applicable by reading the scriptures. Jesus said that after he departed then they would fast.
Matthew 9:15
“And Jesus said unto them, Can the children of the bridechamber mourn, as long as the bridegroom is with them? but the days will come, when the bridegroom shall be taken from them, and then shall they fast.”
You are not supposed to tell others when you are fasting this is between you and God not to get praise of men.
Matthew 6:17-19 King James Version (KJV)
17 But thou, when thou fastest, anoint thine head, and wash thy face;
18 That thou appear not unto men to fast, but unto thy Father which is in secret: and thy Father, which seeth in secret, shall reward thee openly.
In Matthew 17. Jesus also instructs the disciple on how to have more strength with God. He rebuked them for their faithlessness and said...
21. Howbeit this kind goeth not out but by prayer and fasting.