PostgreSQL is implemented using a simple “process per-user” client/server model. In this model, every client process is connected to exactly one server process.

PostgreSQL Connection string

You need to specify the following parameters to connect to PostgreSQL:

• Host or host address
• Port
• Database name
• User
• Password (or other means of authentication, if any)

Example., psql -U <username> -d <database name>

Step by Step:

• The client process requests the master server process called the POSTMASTER process for a connection to the database instance.
• The postmaster process creates a new backend process called the PostgreSQL process after the authentication check is done and if everything is fine, the connection is created.
• The postmaster process will then assign the newly created backend process to the client process.
• Once a connection is established the client process can send a query to the backend (server). The query is transmitted using plain text, i.e., there is no parsing done in the frontend (client).
• The server parses the query, creates an execution plan, executes the plan and returns the retrieved rows to the client by transmitting them over the established connection

Further reading here