One way to overcome our own fears is to give fearlessness to others.
The following passage is from Introduction to Buddhism:
To give fearlessness is to protect other living beings from fear or danger. For example, if we rescue someone from a fire or from some other natural disaster, if we protect others from physical violence, or if we save animals and insects who have fallen into water or who are trapped, we are practising giving fearlessness. If we are not able to rescue those in danger, we can still give fearlessness by making prayers and offerings so that they may be released from danger. We can also practise giving fearlessness by praying for others to become free from their delusions, especially the delusion of self-grasping, which is the ultimate source of all fear.
Introduction to Buddhism is available from Tharpa Publications.