For anyone confused,
In the nominative case (discussing sentence subjects), you use мой (moy) for masculine nouns (that is, nouns that end with a consonant, й, or some words that end in ь)
You use моя (moya) for feminine nouns (that is, nouns that end with а, я, or the other words that end in ь)
You use моё (moyo) for neuter nouns (that is, nouns that end in о or е)
Lastly, you use мои (moi) for plurals.
There are a few exceptions, of course. For example, you say мой папа (moy papa) (my dad), мой кафе (moy kafe) (my coffee), мой дядя (moy dyadeh) (my uncle), мой дедушка (moy dyedushka) (my grandpa), and мой мужчина (moy mushchina)(my man, more like my husband). These are probably the only ones you'll run into in casual conversation.
Just minor correction.
cafe = кафе
coffee = кофе
моё кафе (neuter)
мой кофе (masculine)
As for кофе it is very typical error for many russians to say "моё кофе" as language feeling makes it think about this word as a neuter noun. It was even added to some orfographic dictionaries as neuter and there was wide discussion about it. People who know the correct gender of this word are very proud of their knowledge.
I recommend this odd little website. Put in a word and it will open a new tab with all the conjugations (if a verb) or declinations (if noun) in a helpful and easy to follow table. If it says 'word not found' then you've spelled it wrongly.
There are four different "forms" of "my" in the nominative case(one of six Russian cases, it is used to on verbs which act as the sentences subject). Which one you use depends on the gender/number of the object "my" possesses. For masculine nouns you use Мой, for feminine nouns you use Моя, for neuter nouns you use Моё and for plural nouns you use Мои. I hope this helps. :)
For the curious there's a full table here, under "Declension":
моё молоко - milk has no accent, but, it did in an earlier lesson: Молоко́. There was no mention of accents disappearing in the "Basics 2 - Lessons: Tips and notes", but, it happens to milk in "my milk", and to water, вода́, in "my water", моя вода ? Would someone please explain it to me? Thanks!
ё is io (I think of it as yo), е is 'ye', and э is 'e', as in 'end'. I agree е does often sound like just 'e', but actually it is pronounced 'ye', as in её (yeyo), or нет (nyet).
There is a very good table here: http://www.russianforeveryone.com/RufeA/Lessons/Introduction/Alphabet/Alphabet.htm