You would say "ema" and write it as エマ. (Katakana because Emma is not a native Japanese name.) I would say yor last name as カーライアル (kaaraiaru) Your full name would be エマ・カーライアル (ema kaaraiaru) the extra -a syllable in your last name is to replicate the -ar sounds, but it depends on how YOU pronounce it, but this is the basic way.

As you probably know, foreign names are usually transcribed with Katakana rather than Hiragana in Japanese. Thus your name would be (if I get the pronounciation right): エマ・カーライル /ema kârairu/ or, in eastern name order style, カーライル・エマ. -If you want to write it down using hiragana, it would be: えま ・からいる -You might also try to spell it using Kanji, using them in a phonetical manner called "ateji". You basically select the kanji, which are pronounced like your name. In a fashion similar to that used by Chinese people to spell foreign words. (Just pay attention to the meaning of the characters).

I think it's normally written as エマ・カーライル, in katakana. We rarely write non-Japanese names in hiragana, which would be like えま・かーらいる.