I ate no pleasant bread, neither came flesh nor wine in my mouth, neither did I anoint myself at all, till three whole weeks were fulfilled.
Daniel was mourning and he ate no pleasant bread, nor flesh nor wine. I think this means that he was abstaining from food that he liked (which means he was going on a partial fast). The NIV version says that he abstained from choice food.
Daniel fasted for three weeks. Jesus fasted for forty days and forty nights [Matthew 4:2] and Saul fasted for three days [Acts 9:9].
I believe that we have to examine the reason why we are fasting and decide whether we want to go on a partial fast like Daniel or go on a full fast like Paul. Fasting is really abstaining from a certain type of food and bringing our bodies into subjection for spiritual reason.
I have just posted a topical verse on benefits of fasting:
Hope this helps