Now go back to the Green Cloister in order to take the staircase that leads you to the left nave of the church.
I suggest first going to the "proper" entrance of the church to look at it as if you had entered from the main portal. Only then can you admire all the elegance of this light, bright structure, with its wide Gothic arches supported by spaced pillars. There aren't any chapels along the naves; there are many of them, which are quite rich in works of art, but they are all located at the back of the church.
A famous fresco is on the left wall: the Trinity painted by Masaccio in the first half of the 1400s. It is the painter's last known work, as he died at the very young age of 26. It is considered one of the most important works of the Renaissance for its perfect synthesis of painting, sculpture, and architecture. The figures are arranged so as to simulate a progressive depth.
Another masterpiece is in a dominant position at the center of the Church: the great Crucifix painted by a very young Giotto, around 20 years old, at the end of the 1200s: this is one of the earliest depictions of Christ on the cross in a "natural" position.
Continuing on the left side, I suggest visiting the Gothic sacristy decorated with large wardrobes with golden curls, and at the top of the stairs you'll see the large chapel that I suggest going to see for the paneled painting above the altar and the frescoes on the walls.
I'd also like to point out the elegant wood Crucifix in the chapel in the back, which was carved by Brunelleschi in his early years. In the Tornabuoni Chapel behind the altar, you can admire the Stories of St. John the Baptist, a large cycle of frescoes by Ghirlandaio set in the actualities of the time and quite enjoyable for their lively narrative sense.
...I almost forgot, you also have to go see the extravagant frescoes by Filippino Lippi in Strozzi Chapel.
FUN FACT: Brunelleschi's Crucifix is nicknamed "The Christ of Eggs" for a very funny reason: one of Ghirlandaio's aides for the frescoes in the main chapel was Michelangelo, who was still a child. It is said that when he saw the Crucifix carved by Brunelleschi, he opened his arms in a gesture of amazement, dropping the eggs he had in his apron!