When to use a in Russian?

ы and и this is a completely different letters. However, "и" can be used as a separate part of speech (and). For English-speaking rather difficult to pronounce certain sounds of Russian speech. Try to find a site where there is a sound recording. Otherwise, understand how it is difficult to say.

This is not the most difficult. It will be difficult to learn the signs ь and ъ. These signs are not distinct sounds. However, they show how to pronounce each letter next to which they are located.

You use 'a' when you need to connect two sentences which are not quite opposite, but are not closely connected either.

I am big, and he is small - Я большой, а он маленький.

I drink coffee in the morning and tea in the evening - Утром я пью кофе, а вечером чай.

It was sunny in the morning, but began raining in the evening - Утром было солнечно, а вечером пошёл дождь.

It's somewhere between 'and' and 'but'; it's presenting two separate facts.

As for ы, here is a rather horrible song which should nonetheless help you

http://www.youtube.com/watch?v=S7ZA3UYrG58

In general "a" is used when you enumerate stuff and point out the difference between the items.

Kids wanted toys: Masha asked for a doll, and Misha - for a car.

Here "and" must be translated as "a", neither но nor и fits here.

Marina likes death metal, while Sasha can't distinguish progressive from grindcore.

Here "while" must be translated as "a".

You see, you just enumerate those guys, but the point of the enumeration is to denote the differences in their tastes.