I am trying my first BCFT, and making my first batch of BC.
How long can I store it and how should I store it.

Part of this depends on what you are using to make your buttercream. If you are using an all-shortening recipe, you can store it covered and airtight on the counter for a couple of weeks. I use a half-shortening/half-butter recipe, and it will keep on the counter for a couple of days, but I refrigerate it if I want to keep it for a couple of weeks. I just take it out a few hours before I need it to soften to room temp. I will also freeze buttercream if I want to keep it for months. Just be sure it's well wrapped and get out as much air as you can before freezing. Thaw in fridge first and then transfer to countertop to soften (straight from freezer to counter can produce condensation and make the icing goopy).

Tracey1970 - Thanks for the tips. I am using the 1/2 butter 1/2 shortening. thanks again!

I also freeze mine if I'm not using it the next day. It thaws out really well.