What is the science behind a lit candle?

The processes behind a lit candle are simple and should not be unnecessarily complicated.
A candle is first lit with a matchbox. It causes the melting and evaporation of the wax. It is the vapours of this wax that gets burnt. So, the first doubt should be wiped out that it is not the candle wick but the wax vapours that burns.
Further, the burning process can be simplified to the consideration of only two factors, i.e, oxygen availability and the amount of wax vapours.
At the bottom of the flame, there is abundance of wax vapours but not the adequate oxygen. Therefore, most of the wax vapours remains unburnt and it amounts to the dark colour of the flame at the bottom.
Further, these wax vapours rises up due to convection and gets some more oxygen. However, all these are not able to burn, leading to the formation of soot particles. These soot particles get burned to behave as an incandescent particle and their black body radiation(you can leave this phenomenon at this moment if uncomfortable) produces a yellow glow. The luminescence of the flame is also attributed to the burning of the soot particles.
Now, at the outer edge, there is abundance of oxygen (because of larger surface area) leading to a complete combustion and therefore, the outer cover of the flame is blue.