From all the Biblical references – Old Covenant and especially New Testament, all I see as far as the issue of fasting is concerned is that people eliminated food as they intensely focused on God, often times while seeking guidance before making a strategic decision. In 1 Corinthians 7, marital sexual relations are yet another thing that some people chose to eliminate, along with food, for a period of time:
1 Corinthians 7:5
5 Do not deprive one another except with consent for a time, that you may give yourselves to fasting and prayer; and come together again so that Satan does not tempt you because of your lack of self-control.
In our day, you can add to that list any of the distractions of the modern age, and if you take out some time to intensely focus on God – usually focusing on a specific aspect of your spiritual life or when faced with a strategic decision to make – you simply postpone or eliminate those for a time.