know (one's) way about
1. To be familiar with a particular place or area and be able to navigate around it. I don't know my way about the building yet, so can you direct me to the cafeteria?
2. To know and understand how something works. Thanks to smartphones, you don't need to know your way about a professional camera to take a fine picture these days.
know (one's) way around
1. Literally, to be able to navigate a particular place or area. I don't know my way around the building yet, so can you direct me to the cafeteria?
2. To know and understand how something works. Thanks to smartphones, you don't need to know your way around a professional camera to take a fine picture these days.