which sentence is written properly, "L'herbe est verte" or "L'herbe est vert?"

The difference between the two sentences is the adjective "vert", which varies according to gender and number

vert (masc. sing.)
verte (fem. sing.)
verts (masc. plur.)
vertes (fem. plur.)

Since herbe is a feminine noun in singular, you will choose the adjective , and hence the sentence, that corresponds to the gender and number.

In cases like this, your dictionary is your best friend.