Finally synchronized the blockchain, yet not sure if I'm mining for coins. Where do I find out if I am or do I need something else?
I assume that you have downloaded Bitcoin-QT, the standard bitcoin client. This enables you to manage your addresses, to send and to receive Bitcoin.
If you want to mine bitcoin you will need special software, and if you want to mine bitcoin profitably you will also need special hardware. There is numerous questions about "how to mine with X" on this site, if you want to get started with that. See for example: How can I start mining Bitcoin?