The Russian sound of e is easy, because it is close to ye in English yes. Do not confuse it with English letter e, which sounds like Russian э.
Practice these words:
место лето песня весело
myes-ta lye-ta pyes-nya vye-see-la
place summer song merrily
In the word весело, an unstressed e sounds like an abbreviated Russian и. This rules is called ikanie and it also applies to unstressed я and э.
One must also remember that in unstressed positions, Russian letters Я, Е, Э are pronounced like an abbreviated Russian И.