Three main factors affect the rate of photosynthesis:
Light intensity: Increasing light intensity will increase the rate of photosynthesis, until the maximum amount of light is being absorbed. The main photosynthetic pigment in green plants is chlorophyll, which absorbs red and blue wavelengths (explaining their green appearance). So it's more efficient to use only these wavelengths.
Carbon dioxide: The rate of photosynthesis will increase up to an optimal CO2 concentration of ~0.4% (normal atmospheric levels are ~0.04%). Above 0.4%, stomata begin to close, hindering diffusion into the leaves.
Temperature: 25°C is the optimal temperature for photosynthesis. Below 10°C, enzymatic activity is very low - but above 40°C, crucial enzymes begin to denature (e.g. PSI, PSII, ATP synthase and Rubisco).
N.B. Water and humidity also affect photosynthetic rate. Aside from its role as a source of electrons in the light independent reaction, adequate water absorption by the roots ensures that the stomata remain open (maximizing CO2 uptake). High air humidity also helps keep the stomata open. However, if the soil becomes waterlogged, the root system will struggle to absorb essential minerals.