The "Trema" is a diacritic sign you put on vowel. Usually it is on the e, i, u (and y in proper noun (name of place, family, etc)).

The purpose of its sign is to separate the sound of the vowel. 

<em>For exemple</em> : The word naive in french is naïf
If the double mark isn't upon the i you pronounce : naif (like "nèf" in french pronunciation) 
But with the double mark (naïf), you have to separate this specific vowel and read like that : "na - i - f(e)" 

<em>This is other exemples :</em>

Maïs (corn) :

without double mark : mais = "mè"
with double mark : maïs = "ma - ï - se "

Canoë (canoe) :

without double mark : canoe= "cano"
with double mark : canoë = "cano - e(é)"

Héroïne (heroin) :

without double mark : héroine "oi" like foie, oie, moi, toi...
with double mark : héroïne = "héro - i - ne"

Haïr (to hate) :

without double mark : hair = (same pronunciation than "hair(cheveux)" in english)
with double mark : haïr = "ha - i - r(e)"

<em>But, because it's french language ! There is many exeption like usual !!!</em>

<em>For the moment let's remenber the basic !!!</em>

Exercice :

So now you can try with my name Aloïse, 

how should you pronounce it ?

<em>Good luck</em>