1. Avoid water getting into the internal components
As you probably know, water and electrical stuff do not go together very well. Water may damage the electrical components of the fan and cause it to short circuit! Even if it does not short circuit and continues to work, if the water does not evaporate out and instead gets trapped in there, it can result in corrosion of the metal parts. This will eventually cause the fan to spoil and stop working.
2. Avoid leaving the device on when you do not intend to use it
This one is pretty simple. If left on for long durations when you do not want to use it (like in a bag or left at home), the battery will be drained. The next time you want to use the fan, it will have very little to no power left and you will have to recharge it again, wasting time.
3. Avoid damaging the fan
Again, pretty self-explanatory. While the fan is designed to withstand small drops or knocks, too much physical stress may result in the housing cracking or worse, the entire fan to stop working.