Congratulations! You're now a proud owner of some of my kombucha tea. These instructions should help you build a nice strong culture.
The starter culture
I saved a bottle from my last first fermentation. You should have about 400 ml of tea there. It's pretty strong, I brewed for a bit over 2 weeks so it's nice and tart and should get you off to a good start. I also added a bit of sugar to keep the culture going.
Do not put this in the fridge. the culture will go dormant and will take time to wake back up, and you might end up developing mould in your brew as a result. Until you use the starter culture, keep it at room temperature, and just burp the bottle (open it) daily to let the gas out. Ideally you should use this within a week or so, but you can keep it going for longer by adding some freshly brewed black tea and a couple of teaspoons of sugar. Let it cool down to room temp before adding it to your starter culture otherwise you'll burn it!