Answer:
Concentration - the higher the concentration of the substrate, the more likely it will bind to more enzymes, which will increase the rate of the reaction
Number of particles - similar to concentration; the more particles there are of a substance the more substate-enzyme interactions will occur
Temperature - a bit more complex: high temperatures will denature enzymes and slow the reaction rate almost to a halt; normal/optimal temperatures are the ones at which the enzyme functions the best and the rate of the reaction is highest; too low temperatures won't denature the enzyme, but it will slow down the movement of the molecules themselves so much that the rate of the reaction goes way down simply because the molecules aren't bumping into each other and nestling into the active site anymore
Catalyst - the presence of a catalyst greatly increases the rate of the reaction because that is their job (to decrease the activation energy to speed up the rate of the reaction). It does, however, have to be the right catalyst because the wrong one won't do anything for the reaction (the substrate won't fit, so it won't get acted on, so it's reaction won't get sped up)