When you add yeast to your musts and they begin fermenting the yeasts give off alcohol and CO2. The alcohol remains in the juice while the co2 escapes either on it's own or by stirring.
As it ferments this co2 will help to protect your must from the attack of o2 to your wine. I place (loosely) a lid on top of all of my buckets (primaries) during fermentation. This helps to keep the co2 in the bucket. It also allows for dust, misc. stuff from falling into your bucket yet allows easy access to stir your must daily (or several times daily).
As your fermentation begins to slow due to the low quantity of sugar and nutrients remaining and the increase in alcohol, it starts to become toxic to your yeast and now o2 can begin to make it's way in to begin to oxidize the wine.
It is a dbl. edge sword. Your yeast need o2 yet o2 can harm your wine. When your specific gravity reaches 1.020 to 1.000 (and lower) this is the time you would want to help your wine out.
Either siphon your wine along with all or a good bit of the sediment in the primary or place a lid on top tightly both with an airlock to allow for the co2 to escape but prevent any more air from entering the vessel.
When fermentation has stopped you may now rack to stabilize the wine with sulfite (typically 1/4 teaspoon per 5 gallons) and some may add a fining agent to speed up the clearing of wine.
The problem with your must finishing up in a carboy is it can be a little more difficult taking a sp. gravity reading. Do not believe that as long as you see bubbles coming out of an airlock that your must is still fermenting. It could also be self degassing.
Use your hydrometer to know when fermentation is finished and you may proceed to the next step.
I ferment all of my juices dry in a bucket (normally in 6 days), while others rack to a carboy. As mentioned above it's a matter of personal preferrence. If this is a kit then the times are just guidelines. Follow the directions as given with the kit.