I've been studying Russian for like 3-4 years and I still don't know how to pronounce this word. I see the я and I want to say ya but the more I listen to people speak the more it sounds like vremeh rather than vremya.
If you studied Russian, you should already know that the letter я is not iotized after consonants, so there is no "y" sound there. The word is pronounced [вр'эм'а].
Russian language features reduction of unstressed vowels. This pertain both cases after palatalized consonants or without them, in a different manner.
What is principal here is that м is palatalized, due to presence of graphical я after it. So it results, in general, in pronounciation [ˈvrʲemʲV], where I noted "a non-distinguished vowel" as capital V. But the nature of this vowel could be different: some people say clear [æ] here, as it would be stressed; but for most of rest, a weaker variant closer to [e] is used (maybe with a minor shift to [i]).
So, both [ˈvrʲemʲæ] and [ˈvrʲemʲe] are correct here. But, replacement of [mʲ] with [mj] (suggested by your "vremya") is definitely foreign and hints on hearing a non-trained learner.
more it sounds like vremeh rather than vremya.
If you have hesitations in pronounciation, you'd better use IPA symbols than such "indirect" descriptions which are good among a single language but not studying a really foreign one.
I highly recommend using the Forvo service. You can listen to different voices: https://forvo.com/word/%D0%B2%D1%80%D0%B5%D0%BC%D1%8F/#ru
Оne of the methods to learn how to pronounce such words is to divide them into syllables. "Вре" + "мя" or "В" + "ре" + "мя"(even better). Learn to pronounce them separately. A common problem for English speakers is not to say "время" but "времЬа". "Я" is pronounced similar to "ьа", but still in a different way.