How can I find expansion coefficients of the y vector in a given basis?
You need to find projection of $\vec{y}$ along unit vectors in the direction of each of the basis vectors $\mathbf v^{(i)}$. 

For finding unit vector in the direction of the vector, you just divide the vector by its magnitude.

And, for finding projection along a unit-vector, you just take the dot-product with the unit-vector.

So, the combined steps boil down to doing the following: $$&lt;\vec{y}, \frac{\mathbf v^{i}}{||\mathbf v^{i}||^{2}_{2}}&gt;$$

In your case the basis-vectors are already normalized, meaning they are already unit vectors, so just take the dot-product(inner product) of vector $\vec{y}$ with each of the basis vectors $\mathbf v^i$