With the Cloud Connector Connection Manager (a MMC snap-in) you have to setup:
1. the connection (e.g. uni-directional with overwrite, scheduling etc.),
2. the data source (your Intranet view ToExtranet) and
3. the data destination (in Extranet, the library must be created manually before).
You can use auto mapping to connect the fields of both data entities or map fields manually.
See here for sample connection settings:

Fig.: Sampe Intranet-to-Extranet one-way connection.
Please note:
- Bi-directional connections are supported as well, if required.
- If overwrite destination is enabled, non-matching entries in the destination are removed with initial sync.
- Please enable schedulung later on, when all settings are verified and you have an idea of replication duration. Duration time depends on bandwith, performance of source and destination, document size and number of documents. Only changes are transferred.
Before running the connection, you have to define the data source and destination.

Fig.: The CSOM Provider is used to connect to the data source, e.g. a SharePoint on-premise.
Please note:
- The view "ToExtranet" is given as data source in connection string.
- Windows authentication is used to connect to the Intranet.
- You don't have to enter a primary key, SharePoint document IDs are used by default.
- Please verify all settings before save.
- The data source could also be in the cloud. Cloud-to-Cloud conenctions are supported as well.
Next you have to define your data destination:

Fig.: Data destination sample, a library "Extranet" in the Office 365 cloud.
Please note
- The destination can be an on-premise SharePoint as well or any other hosted SharePoint 2010 sandbox.
- No installation required on both sides, source and destination. The Cloud Conenctor runs somewhere in your network as a windows service, e.g. on any Windows Server or Client (Windows 7).
If all settings are verified, please go to connection root and run the connection manually first. Please note,that it cloud take some time to transfer all documents. You can take a look in your cloud library to see how it goes on.