It is important to first correct any colour issues with your footage before you move on to colour grading. Otherwise it's like putting fresh paint on your walls without a proper undercoat.
Also note that colour grading can technically 'break' your colour correction again, but that's ok; properly correcting any colour issues beforehand ensures that we have the best possible starting point when it comes to grading our footage.
Colour Grading is the process of creatively altering the appearance of your footage to give it the desired emotional impact. You might want a scary movie to look dark and gritty whereas a comedy should probably look more colourful and happy. How you colorise and style your footage has a huge impact on how the audience will experience it. For example, here is the same scene, once made to look warm and friendly and once made to look all scary and dark.
While I will use Adobe After Effects for this tutorial, you should be able to follow along with any other video editing or visual effects compositing software as long as it offers you effects to control the colour of your footage and apply some creative effects.
Let's get started!