Hold your mouth very open, with your jaw loose. You can say 'a' like this, but you can't say 'e'. Now try to force yourself to say 'e'. You'll find that the only way you can say it is by closing your mouth slightly and widening your 'smile'. Does that help?

The most successful method I've found for teaching the æ sound is to treat it like two syllables at first. There's a reason that symbol is made of two vowels pressed together--that's how we form the sound. However, we do it so quickly that it becomes one mashed syllable. In the Southern United States, where I was raised, many people pronounce 'and' with two syllables. It sounds something like 'A-end'. If you begin with that, it trains your mouth to form the correct shape. Over time, shorten those two syllables until it's a single sound. Koreans have the same trouble with these sounds, and they have a similar sound that falls right between them, so it's similar to Russian. The method I described has worked for many of my students. Just remember that natives aren't born with perfect pronunciation, either. We make a lot of mistakes until we get it right.

Suki's advice is great. Also, be careful of the sound at the end of the syllable.. if it's a nasal sound (n or m), US speakers will tend to diphthong it as /áe/ (or worse) in the South, or as /éa/ (or worse) in the rest of the US. If on the other hand, the last letter is an unvoiced consonant like t, p, k, f, sh, s, the vowel will be shortened an may be too quick to hear. Also, forget about syllables ending in "r." I recommend using the words the pair head [hɛd] versus had [hæd]. To be perfectly frank, avoid imitating US or Canadian speakers if you really want to get this sound right.

В слове "man" буква "a" ближе к русскому "э", т.е будет произноситься как "мэн". В слове "men" - русское "е", т.е "мен". Во втором случае получится более мягкий звук, примерно, как в слове "мера".