Kuba,
it is not the same sound. Since every French word is oxytone, accent mark doesn't indicate the stressed vowel but just its sound. So...
«e» is /ə/ (or mute if at the end of the word)
«é» is /e/ (closed «e», toward the sound of «i»)
«è» is /ɛ/ (open «e», toward the sound of «a»)
emphasizing it, try to say "e" closing your mouth and then again opening your mouth and you'll will hear the difference.

The best way to learn them is to read a lot. As a Pole I don't see any rule, regarded to the accents. But I see, that some accents are related to the sound of the vovel. In Polish we have also such issue, with u and ó or h and ch which have the same sound but only separate form. The only way to learn them is to read written texts.

Thanks for all your answers:-) I think I must learn them by heart. I don't think I'll ever be able to hear rhe difference between two Es. Carmelo, remember your problem with Č and Ć in serbian, this is the same:-(, I just don't have an ear good enough. Peachey, my exemple with être was to make my point that with one so basic verb there are different accents over the E. In prononciation I do not hear the difference and I think that phonethic is not "reachable" for me yet on this level of french.

There is the same rule that in Italian is: grave over open "e"s /ɛ/, acute over closed "e"s /e/
As you write "tè" (tea) and "è", but "sé" and "né"... you write "été" but "lève" (je me lève) and also "élève".  

Yes, Ivana, I remember that problem. It is why I want to solve this one! ;-)
Can you hear the difference between "pésca" (fishing) and "pèsca" (peach), or between "légge" (law) or "lègge" (he/she read), or between "vénti" (twenty) and "vènti" (winds)? If yes, the penny has dropped! :-)
If no, I'll give other three till you'll find the ones you can hear... :-P