The Connect method will initiate a connection between the local computer and the server. Once the socket is connected the handshake starts:

• Both the server and client exchange version identifications. See RemoteId and Client properties.
• The session key (shared secret) is jointly established using the Diffie Hellman (DH) key exchange. See KeyExchanges property.
• The symmetric key algorithms for the data encryption are negotiated. See Encryptions property.
• The compression algorithm is negotiated. See Compressions property.
• The user authentication starts. See Authentications property.

At this point the SSH session is established and the clients opens a new channel with the "sftp" subsystem. 

For further information see RFC 4253 - The Secure Shell (SSH) Transport Layer Protocol.