How can I create notification on user's connecting to database?
There are three ways to find who is connected to a database in sqlserver. 

First one:

Use the SQL SERVER Management Studio -- Management -- Activity Monitor
This gives a list of users, database names, status, command, transactions, application with which they are using the database, CPU, IO and Memory usage, Login time etc.

Second One:

Use the built in stored procedure called sp_who2
Run the command exec sp_who2
This gives a list of users, database names, status, command, program with which they are using the database, CPU time, Login time etc.
Third One:

Third one Use the script

DECLARE @temp TABLE(spid int , ecid int, status varchar(50),
                     loginname varchar(50),   
                     hostname varchar(50),
blk varchar(50), dbname varchar(50), cmd varchar(50), request_id int) 
INSERT INTO @temp  

EXEC sp_who

SELECT COUNT(*) FROM @temp WHERE dbname = 'DB NAME'


From the above methods, you can use them to implement in a sql job to get required notification.

The best method i used is the latest sp_whoisactive by MVP Adam Machanic