Worship is different for everyone, and is influenced by whatever "path" you choose be it Wiccan, Druid, Heathen, etc.
I know almost nothing about the Egyptian pantheon, but since you've chosen Bast as a patron goddess I assume that you do. To make a shrine, set up a space that is relatively out of the way so that no one will accidentally bump into it and break whatever you choose to put on it. In your shrine space you could have a statue of Bast and various other things representative of Bast as a way to start out. As for how you would go about your worship of Bast, that should be unique to you. Research Bast and worship her however it feels right to you. When working with a deity, they will reveal to you how they like things.
Hopefully that helps a little bit..?