God answers are pryers in many ways but to address three of them.
God answers prayers by using his Holy Spirit, to :
Affect our attitude or the attitudes of others.
or He uses
If our prayers are answered directly then God will provide i=us the wisdom to make the proper decision.
If our prayers are answered indirectly then Jehovah God will move someone by his holy spirit to act on our behalf.
And of course Jehovah can choose to use his mighty Angels to help us. And his Angels have the power to move mountains.