The antidote to fear is a combination of love and trust in that which is good and powerful.
I find that what works best as a start is to concentrate on the here-and-now - in other words self-remembering; because fear is about the future. This can then be followed-up by reflection on the fact that God is the creator of this world, who is our loving Father, therefore can be trusted to do whatever is necessary and possible.
Another source of fear is about whether we ought to be doing something to prevent the feared from happening, but what? And how can we be sure what is for the best?
This is when self-remembering can be followed by seeking the guidance of the Holy Ghost, who will tell us here-and-now what, if anything - and often there is nothing - should be done. This obviates the guilt pressing us towards that obsessive but fruitless planning, which plagues modern Men.
John Butler is very good on the specific business of detaching from abstract and theoretical angst; and becoming aware of oneself in the here-and-now; and (at his quietest) has just about the most soothing voice I've ever heard! - This immediately takes the sting out of present fear, and can be used to lead-into the process described above:
