How to give permissions for executing a procedure to specific database user?

Problem: How to give permissions for executing a procedure to specific database user?

Solution:  GRANT

Grants permissions on a securable to a principal. The general concept is to GRANT <some permission> ON <some object> TO <some user, login, or group>. For a general discussion of permissions, 

To know more about a database user please go through this article. What is a database user

Syntax:

   GRANT { ALL [ PRIVILEGES ] } 

      | permission [ ( column [ ,...n ] ) ] [ ,...n ] 

      [ ON [ class :: ] securable ] TO principal [ ,...n ]  

      [ WITH GRANT OPTION ] [ AS principal ] 

Example:

In this example, I would like to show we can Grant a user to execute on a procedure to a newly created role.

CREATE ROLE proc_tester

GO

GRANT EXECUTE ON [dbo].[UpdTableBbyDate] TO proc_tester

GO

ALTER ROLE proc_tester ADD MEMBER TestUser

GO

--query to see the roles and members are added.

select u.name as Rolename,u1.name as membername from sys.database_role_members m

INNER JOIN sys.database_principals u

ON m.role_principal_id=u.principal_id

INNER JOIN sys.database_principals u1

ON m.member_principal_id=u1.principal_id

where u.name='proc_tester'

Results:

Rolename	membername
proc_tester	TestUser