How can I ensure the white balance is correct?
It depends on your camera.  Some cameras, like the Blackmagic cameras only let you guestimate.  In this case, you'll just have to know that the color temperature of an outdoor scene is closer to 5600K, warm tungsten light is closer to 3200K, etc.  Then, you'd adjust the image in post to make it more accurate.  Using an x-rite color chart with software like Davinci Resolve (free lite version) can speed, simplify, and improve your results.

Other Cameras, like the Canon 5D Mk II and III will let you place a white or grey card in front of the camera, snap a photo, and internally analyze the color.  I recommend consulting your camera's manual to see if it supports this functionality.

But if none of the above work for you, and you're looking for something like a histogram to analyze the color, you could look into vectorscopes and waveform monitors.  Hardware versions can be pricey, but cheap software versions are available.  Scopebox is a good one for mac.  Maybe someone can comment on a good PC one.  With this solution, you will need a hardware device to convert your video signal to something your computer can read (HDMI to Firewire, SDI to Thunderbolt, Composite to PCIe, for example).  To be clear, this is just a monitoring solution.  In other words, a vecrorscope/ waveform monitor won't change the color of the signal, but it will let you adjust it accurately at the camera, much like you would use your camera's histogram to set exposure.