Which notation, methodology and tools for database creating, modeling, diagraming you want and why?
Which notation, standards, methodology would be the most broadly used and included in different suppliers?
That are standard and which aren't ?
i.e. that are to stay with and which to prevent

And private question to PerformaneDBA:
So why do you want IDEF1X?
Isn't it much more comfortable to stay with tools, notations built-in into used client tools of RDBMS?

Update:
Someone said What are some of your most useful database standards?.
I'm quite surprised - dozen of solutions there and simply no names or references, only extended explanations.
Are database designers amateurs using custom-made terminology and conventions?

I up-to-date the title including "title" and excluding "methodology".
Things I requested was names (possibly references) not explanations.
Notations, for ex., UML, IDEF1X. Barker, Information Engineering

Well, I'm mostly SQL Server dev and, as @dportas pointed out, I see some notation in diagrams in SSMS and msdn paperwork, books, articles.

For ER models I favor the IEM or Barker style simply because I've found more people comprehend the crow's ft notation. If you prefer a model to become understood with a wider audience than yourself then it seems sensible to utilize a recognised standard notation.

For database vendor tools, that is dependent. I have never thought it was necessary to use any particular tool, except in which a customer had been one. Oracle and Sybase have decent diagram tools. Microsoft Visio props up standard notations, although like a database design tool it is not as effective as numerous others.

The only real really bad example I'm able to think about may be the so-known as design tool included in the Microsoft SQL Server toolset. It is simply a tale. Completely useless for just about any serious purpose and I'm not sure anybody who uses it except in Microsoft guides.