How do I see active SQL Server connections?

I am using SQL Server 2008 Enterprise. I want to see any active SQL Server connections, and the related information of all the connections, like from which IP address, connect to which database or something.

Are there existing commands to solve this issue?

You can use the sp_who stored procedure.

Provides information about current users, sessions, and processes in an instance of the Microsoft SQL Server Database Engine. The information can be filtered to return only those processes that are not idle, that belong to a specific user, or that belong to a specific session.

SELECT 
    DB_NAME(dbid) as DBName, 
    COUNT(dbid) as NumberOfConnections,
    loginame as LoginName
FROM
    sys.sysprocesses
WHERE 
    dbid > 0
GROUP BY 
    dbid, loginame
;

See also the Microsoft documentation for sys.sysprocesses.