Where can i get the step by step expression for CMB anisotropy? I never able to wrap my head around alm term used in expression 
If you know the expression, kindly explain but also give textbook references. It would be helpful.
 A: Any function on a sphere can be expanded as a linear combination of spherical harmonics $Y_{\ell m}$. The numbers $a_{\ell m}$ tell you “how much” of each spherical harmonic is needed. This is similar to a Fourier series for decomposing any periodic function $f(x)$ into its sinusoidal “harmonics”.
Conceptually, the spherical harmonics are a complete orthonormal basis for the infinite-dimensional vector space of functions on a sphere, in the same way that $\mathbf{i}$, $\mathbf{j}$, and $\mathbf{k}$  are a complete orthonormal basis for three-dimensional Euclidean vector space (and in the same way that $\cos{nx}$ and $\sin{nx}$ are a complete orthonormal basis for periodic functions in one dimension). The $a_{\ell m}$ are the components of $T$ in this basis.
One classic reference book for such things is Methods of Mathematical Physics by Courant and Hilbert.
The book or paper you referenced has a typo. They meant that the $a_{00}$ term measures the mean temperature. This is because the first spherical harmonic $Y_{00}$ is a constant over the sphere. The other terms represent angular fluctuations in temperature around the mean, on smaller and smaller angular scales as $\ell$ increases.
