Noting that each tends to have its own standard...
I found a good place to start to remember different computer languages was to quickly see if the chosen language is case sensitive, and if so are the methods upper/lower and does this depend on them being static/instance, I know you already understand this
It follows, check for variations between classes and methods...
eg C#.NET will GetKey, python will get_key, ecma/java/action script will getKey, VB.NET doesn't give a crap if you GetKey or getKey.. or even GeTkeY...
seeing as all the above (except VB, WTF V'f'n'B!) are case sensitive, so you can start to guess, this is the stuff you need to memorize right off the bat, intellisense is often case sensitive and context senstive (static v instance)
I expect you know this, but,
"javascript", id's are often cased Id not ID, but HTML not Html - document.getElementById('Id').innerHTML
So you condition yourself, you say, I'm in javascript, that's a lowercase d on Id, I'm in .NET so the acronyms Html, Dns. not as in JS where they are HTML, DNS
The answer to the memory/IDE question, yes you still need to use your memory, but I find intellisense moves the memory task from which method name, to which bit of the framework/namespace, i.e. in .NET was that Base64 function in System.String or Convert.ToBase64.. or System.Text...
One of the main reasons to use an IDE is debugging, the ability to set breakpoints visually and single step though the code, real coders use the debugger to actually debug, not as a code crutch
IDEs give rise to the concept of projects and structure, and several have awesome version control plugins. The source code highlighting is 'usually' heaps better than TextMate/Emacs/Notepad or whatever
IDEs often allow for click navigation to a given class/method (ctrl click)
IDEs often help you find references to/or obsolete bits of code
IDEs often automagically format your code (shitty indentations, tabs v spaces) this can be viewed as good or bad
IDEs allow for templated solutions, i.e. eclipse can set you up well on the way to a django google apps project, without any typing, the file/editor based alternatives involve copy/paste reuse...
Lastly you just practice and get it wrong a lot of times until you remember and thenyou get it right.
final thing on new programming languages, is it dynamically typed...
oh = "yeah", var oh = "yeah", oh:"yeah"
or strongly typed
string oh = "yeah", oh as string = "yeah"
If you know how the language is meant to behave and learn the suggested naming conventions for the given language, then remembering the method names becomes a whole lot easier
def getNote(): return some.dark.and.really.obscure.namespace.to.get_one_note_by_googling.for_an_answer_function()