How do I get my on chain BTC into the zap wallet / lightning? Can I send money from a regular Bitcoin wallet into this lightning wallet?
You have to open a channel with some Lightning Network node in order to be able to spend your coins over the LN. You should be able to create a new channel under "Channels" in the top-right corner. You should see a list of recommended nodes. Since you don't have any prior experience, choose one of them; it will be much easier for you. You have to fund the on-chain address of your Zap Wallet first.
Note that you won't be able to refill that channel directly from your wallet. Make the channel big enough if you want to use it more than a couple of times. Also, you won't be able to receive payments right after opening the channel. You can read the explanation
here.