Pace - just for you I have kept it simple
Bergeron Process - Geography For Kids - By KidsGeo.com
But if you google 'bergeron process' you will find plenty of answers - wikipedia has enough science for you I suspect.
You will see that, as I have indicated in previous posts, supercooled droplets (of varying sizes and formed on the condensation nuclei) co-exist with ice crystals (formed on the freezing nuclei) and the water evaporates making the ice crystals grow (into snow).
In the UK, sleet (referred to as RASN) is snow that has melted on its descent to Earth and accompanied by snow that has yet to melt. In the US, sleet is snow that has melted and re-frozen into solid, non crystalline particles.
Hope this helps.