I've left properties and methods to the end because they are already well documented in the official docs. They are really just here for completeness. If you have worked with the Date object in a previous version of Actionscript then there is one point worth mentioning. You are probably used to working with methods like this:

var hours = d.getHours() // and d.setHours(5)

Although all these legacy methods are still available to you, you might want to consider moving over to the property syntax. This is new in AS3 and much cleaner to use. The property equivalents of the above methods look like this:

var hours:Number = d.hours // and d.hours = 5

These new properties make the get() methods largely redundant but the set() methods can be still be useful as most of them take multiple parameters; for example the full setHours() syntax looks like this:

setHours( hour:Number, minute:Number, second:Number, millisecond:Number ):Number

Properties and methods
At the risk of stating the obvious, any property or method marked as UTC will return or set a value in UTC; anything else is in local time.

Milliseconds: the number of Milliseconds as an integer between 0 - 999

milliseconds:Number millisecondsUTC:Number
setMilliseconds( millisecond:Number ):Number
setUTCMilliseconds( millisecond:Number ):Number

Seconds: the number of Seconds as an integer between 0 - 59

seconds:Number
secondsUTC:Number
setSeconds( second:Number, millisecond:Number ):Number
setUTCSeconds( second:Number, millisecond:Number ):Number

Minutes: the number of Minutes as an integer between 0 - 59

minutes:Number
minutesUTC:Number
setMinutes( minute:Number, second:Number, millisecond:Number ):Number
setUTCMinutes( minute:Number, second:Number, millisecond:Number ):Number

Hours: returns the number of Hours as an integer between 0 - 23

hours:Number
hoursUTC:Number
setHours( hour:Number, minute:Number, second:Number, millisecond:Number ):Number
setUTCHours( hour:Number, minute:Number, second:Number, millisecond:Number ):Number

Day of week: returns the day of the week as an integer between 0 - 6
(0 = Sunday, 1 = Monday, 2 = Tuesday, 3 = Wednesday, 4 = Thursday, 5 = Friday, 6 = Saturday)

day:Number dayUTC:Number

Day of month: returns the day of the month as an integer between 1 - 31

date:Number
dateUTC:Number
setDate( day:Number ):Number
setUTCDate( day:Number ):Number

Month: returns the number of Months as an integer between 0 - 11
(0 = January, 1 = February, 2 = March, 11 = December)

month:Number
monthUTC:Number
setMonth( month:Number, day:Number ):Number
setUTCMonth( month:Number, day:Number ):Number

Year: returns the Year in the Gregorian calendar as a 4 digit integer

fullYear:Number
fullYearUTC:Number
setFullYear( year:Number, month:Number, day:Number ):Number
setUTCFullYear( year:Number, month:Number, day:Number ):Number

Strings:

toDateString():String
toLocaleDateString():String
toString():String
toLocaleString():String
toUTCString():String
toTimeString():String
toLocaleTimeString():String