I'm having trouble with understanding how to differentiate between these two words (eine/einer) in german. I understand their grammatical significance and meaning. But when I listen to german I can hear no difference so it takes me a while to understand what I'm listening to. Is it just a matter of looking at the context?
And I also wanted to know if, when speaking german, I should be putting much emphasis on the 'r' on 'einer'? It obviously does change the meaning but when I do put on the emphasis, it doesn't seem to sound very natural to me.
Any help is much appreciated. Thank you :)

eine - IPA: /ˈʔaɪ̯nə/
einer - IPA: [ˈʔaɪ̯nɐ]

So, even if you don't read IPA (Which I greatly recommend for such things) you can see that there is no 'r' at the end of the word. That's because the -er in this position is making a different sound. So, you're looking at two vowel sounds.

What is natural is a relative thing. Yiddish, a closely related language to German, certainly pronounces the r on the end of this word. :)

On http://dict.leo.org/ende?lp=ende&lang=de&search... you can listen to the pronounciation of "einer, eine, eines". Click on the speaker symbol behind "einer, eine, eines". You can clearly hear a difference. The "e" sounds different. I would say that there is not much emphasis on the "r" in standard German. To me it sounds more like a gutural sound. But depending on the region and the accent people will put less or more emphasis on the "r". In the south of Germany you will often find people who "roll" the "r".

Vielen Dank guys :D
Much appreciated :)