Given that density altitude is a function of Pressure, Temperature, and Humidity, and most takeoff performance charts adjust takeoff distance as a function of pressure altitude and temperature, how is the humidity effect on density altitude taken into account?
Add 10% to your computed takeoff distance if it is too humid.
Humidity. Humidity is not generally considered a major factor in density altitude computations because the effect of humidity is related to engine power rather than aerodynamic efficiency. At high ambient temperatures, the atmosphere can retain a high water vapor content. For example, at 96°F, the water vapor content of the air can be eight (8) times as great as it is at 42°F. High density altitude and high humidity do not always go hand in hand. If high humidity does exist, however, it is wise to add 10 percent to your computed takeoff distance and anticipate a reduced climb rate.
Source: Density Altitude, FAA, 2008, faasafety.gov
It's worth noting that Airbus makes no mention of humidity in their performance guide, Getting to Grips with Aircraft Performance. So simply follow the FAA's advice, and any correction factors mentioned in your aircraft's flight manual.
Temperature and humidity both affect air density and engine power. $H_2O$ molecules are lighter than the $N_2$ and $O_2$ molecules they displace in a volume of humid air.
1. Air Density. The graph below from this site shows that at 40°C, which is a high atmospheric temperature, dry air is about 0.94 density at 20°C, while 100% humidity reduces the density to about 0.91, a 3% reduction. The Standard Atmosphere references temps of 15°C, so the relative density reductions would be 0.92 for dry air and 0.89 for 100% moist air.
2. Engine power. Again from prof. Wittenberg's 50-year old uni book, the effects of humidity and temperature on engine power. Note that particularly piston engines are affected by humidity, turbojets & -fans not so much because they operate with a large over-ratio of air. Temperature affects a turbojet engine much more than a piston engine - the graph line is for a pure turbojet though, a modern high bypass fan engine graph would be much closer to the piston graph.