If video footage is not shot under the same exact circumstances, correction and grading will need to be done in post. For the most part, the following steps will need to be undertaken to convince an audience that a scene was shot at the same time and place.
1) Base Correction Stage a) pick a "hero shot" from the set of scenes and set your exposure values (gamma, gain and lift) with help from the waveform meter, b) modify the contrast values using gamma curves to your liking, c) colour balance with help from RGB parade and vector scopes keeping in mind people's skin tones are most important, d) match the shots from the rest of the clips to your "hero shot" by split screening.
2) Build your Look a) determine the mood the scene requires, b) determine the time of day, c) consider and build in the context of the scene, d) is there a popular look you wish to copy?, e) is there a stylized look the scene requires?
3) Secondary/Isolation a) using masks, clean up any details in the clips (exposure problems, skin smoothing etc) again with masks, focus attention where you want the audience's attention.
Correction and grading can make or break video footage, no matter how creative or imaginative the script, work of the director or DP. Poor shot-to-shot matching is probably the biggest sin no matter how many ungraded or uncorrected youtube, iPhone and GoPro videos the audience has seen.