They gain Kinetic Energy which means they more quicker so there's going to be more collisions.
It also increases the energy of the collisions. Reactions only happen if the particles collide with enough energy. At higher temperatures there will be more particles colliding with enough energy to make a reaction happen.
More particles of reactant in the same volume, which makes collisions more likely. The frequency of the collisions increases.
Breaking a solid into smaller pieces will increase it's surface area.
Increasing the surface area will mean that the other particles have more area to collide with, which means the frequency of the collisions will increase.
Gives the reacting particles a surface to stick to where they can bump into each other. It reduces the energy needed by the particles before they react. More successful collisions.