This has been the subject of discussions on many forums over recent years. I realized that there were all sorts of tutorials offering often conflicting information regarding the process. This is not the only way, just my way. I would like to thank my mates Ben Cowell and Phil Shoebottom for offering some clarity on a few points.
What is "Linear Workflow"?
Look at Fig.01. What is the difference between the image on the left and the image on the right? The truth is; nothing at all, except the way your monitor is showing you the image.
V-Ray and 3ds Max process the data in which to make an image in "linear space", also known as Gamma 1.0, but by default all monitors show you the image with a Gamma of 2.2 (sRGB), which basically makes the image look dark, although it actually isn't dark at all. The program just assumes that you are viewing the image with Gamma set to 1.0, instead of 2.2, until you tell it otherwise.
Unfortunately this has always been the case with 3D rendering, which means that many artists who don't know about linear workflow learn to light scenes by using a handful of tricks to try and get results you'd expect in real life. Things like adding more lights, boosting the Environment/GI levels to incredibly high values, adding some ambient lights with shadows turned off, etc. This all adds to the amount of calculations being made by the renderer for no real reason, as all of the data is in fact already there, providing you tell the program to show it to you correctly.
Setting up 3ds Max
As well as the image itself, textures and materials also need to be correctly converted to Gamma 2.2. Note that V-Ray will ignore all of the Gamma settings in the 3ds Max dialog. We do this step in order to set up the Material Editor to render its thumbnails with linear workflow so that we get an accurate representation of what materials in our render will look like. It's worth noting that you can render in linear space in V-Ray without touching these setting at all, but you won't be able to use the Material Editor thumbnails to accurately tune your shaders.
Go to Customize > Preferences > Gamma and LUT. Change the settings to those shown in Fig.02.
As I said, V-Ray ignores the Gamma settings, but it doesn't ignore the Input Gamma in the Bitmap Files box. By setting this to 2.2 you will globally effect how textures are loaded in. Don't change the Output Gamma as this will burn in the Gamma correction to rendered images, which limits what you can do to the image in post.
Most images you find on the internet or from your digital camera will be sRGB (Gamma 2.2) already so it is just easier to assume 2.2 from the beginning. Some files are natively linear (like HDRIs) so will not require correcting to 2.2; you also do not want to correct Normal maps or Displacement as they won't work properly. For these images the best thing to do is override the Gamma settings on a case by case basis as you import them into your scene (Fig.03).
3ds Max is now set up correctly, so set up your scene and create a render using the V-Ray Frame Buffer.
Setting up V-Ray
First step, go to V-Ray's Color Mapping dropdown menu, change the Gamma to 2.2 and tick Don't affect colors (adaption only) (Fig.04).