what the original poster calls a "group" is what books on line calls a "role". you typically create a role and add the expected rights tot eh role, then add users to the role.

here's a nice script i like to use as an example:

create database Whatever

GO

USE Whatever

CREATE ROLE [ReallyReadOnly]

--give reader rights to this group

ALTER AUTHORIZATION ON SCHEMA::[db_datareader] TO [ReallyReadOnly]

--explicitly DENY access to writing

ALTER AUTHORIZATION ON SCHEMA::[DB_DenyDataWriter] TO [ReallyReadOnly]

GRANT EXECUTE TO [ReallyReadOnly]

--create the Role for my Dev guys, who create tables and procs

CREATE ROLE [WhateverDEVAdmins]

ALTER AUTHORIZATION ON SCHEMA::[db_ddladmin] TO [WhateverDEVAdmins]

ALTER AUTHORIZATION ON SCHEMA::[db_datareader] TO [WhateverDEVAdmins]

ALTER AUTHORIZATION ON SCHEMA::[db_datawriter] TO [WhateverDEVAdmins]

GRANT EXECUTE,ALTER TO [WhateverDEVAdmins]

--create role for my normal users

CREATE ROLE [WhateverDEVUsers]

ALTER AUTHORIZATION ON SCHEMA::[db_datareader] TO [WhateverDEVUsers]

ALTER AUTHORIZATION ON SCHEMA::[db_datawriter] TO [WhateverDEVUsers]

GRANT EXECUTE TO [WhateverDEVUsers]

--now add specific users to nearly-Admins

IF NOT EXISTS (SELECT * FROM MASTER.dbo.syslogins WHERE name = N'bob')

BEGIN

EXEC MASTER.dbo.sp_addlogin @loginame = N'bob', @passwd = 'NotARealPassword', @defdb = N'WHATEVER', @deflanguage = N'us_english'

--add this user to permit read and write

END

IF NOT EXISTS (SELECT * FROM MASTER.dbo.syslogins WHERE name = N'jeff')

BEGIN

EXEC MASTER.dbo.sp_addlogin @loginame = N'jeff', @passwd = 'NotARealPassword', @defdb = N'WHATEVER', @deflanguage = N'us_english'

END

USE [WHATEVER]

--make a user in the db for the matching login

CREATE USER [bob] FOR LOGIN [bob]

CREATE USER [jeff] FOR LOGIN [jeff]

--add these logs to the role

EXEC sp_addrolemember N'WhateverDEVAdmins', N'bob'

EXEC sp_addrolemember N'WhateverDEVAdmins', N'jeff'

CREATE LOGIN [NT AUTHORITY\Authenticated Users] FROM WINDOWS WITH DEFAULT_DATABASE=[WHATEVER]

CREATE USER [NT AUTHORITY\Authenticated Users] FOR LOGIN [NT AUTHORITY\Authenticated Users]

EXEC sp_addrolemember N'WhateverDEVUsers', N'NT AUTHORITY\Authenticated Users'