First start with the equilibrium equation:
Le Chatelier's principle states that a system at equilibrium will move to counter any imposed changes. Roughly speaking, if you push it one way it will push back the other way.
1. Temperature
If we raise the temperature of the system then the system will attempt to lower its temperature. Since the forward reaction is exothermic, the endothermic back reaction (LHS) would therefore be favoured as an endothermic reaction will lower the temperature of the system. Therefore carbon dioxide comes out of solution at higher temperatures.
2. Pressure
If we raise the pressure of the system then the system will attempt to lower its pressure. The side with the least pressure is the RHS (since you have a gas on the LHS), so the system will move to favour that side. Therefore carbon dioxide dissolves more at higher pressures.