Your node connection details will be available at the bottom of your Stellar node dashboard once your node has synced.

Note: With the new Horizon 1.0.0 update, it can take up to 2 hours for a Horizon ledger ID to populate. 

Copy the connection script (shown above) and paste it into your terminal program to instantly connect to the shared node.

You’ll then need to connect with the Horizon server.  What is Horizon? 

Go to the Horizon Reference Overview for libraries to interact with Horizon.

How to use the SDK’s on a Stellar node: https://blockdaemon.com/docs/protocol-documentation/stellar/how-to-use-sdks-on-a-stellar-node/