I am using buttons in one of my project..
Does that involve clothing? If it's an electronic project, switches would be more appropriate.
Please give me an idea how to set the timeout of the button press...??
You can't.
What you need to do is record when the "display the menu" switch was pressed. Record when any subsequent "interact with the menu" switches are pressed.
Periodically, see if now (millis()) minus then exceeds some value. If so, change what the Arduino is doing (take the menu down).