First, choose the formula that is right for you're purpose and your skin texture in the area being concealed (i.e. covering under eye circles, blemishes, or bruises will require different formulas for different areas of your face or body. Longwear concealers that are liquid will finish differently than a cream or stick concealer) And make sure your face is clean, moisturized sufficiently, then dry, and that you've applied an appropriate eye cream.
Second, Choose a shade that will compliment that purpose (i.e. hiding under eye circles requires a shade that cancels blue or purple, usually a slightly peachier color than your foundation would be, while hiding a blemish usually needs to be true to the color of your skin or slightly ashy if its raised and red.)
And Third, acquire the proper tools to accomplish your mission. I always use a flat concealer brush to apply the product then I finish the look by blending it out with a Tapered Blending Brush. I have two that I use, the #286 from MAC which is light and feathery and the #224 which is just a slightly denser brush for blending heavier applications. Feathering lightly in a circular motion will magically and evenly distribute and blend your concealer so that it looks flawless and virtually undetectable.
Last but not least Its important to always apply your concealer AFTER you apply your foundation which prevents smearing it off and then set it with your powder last.
Ive attached a photo of some "Tapered Blending Brushes". This is roughly what they should look like.
Hope this helps people! Im always happy to answer any questions, feel free to message me anytime.