Using of substitution method I am learning that how recurrences solve and I try to use substitution method in this question:
$$T(n) = 3T(n/2) + n^2$$
What should be my guess ?

Enforce $n \mapsto 2^n$. We have,
$$T(2^n)=3T(2^{n-1})+4^n$$
Now define $f(n)=T(2^n)$. So that now we have,
$$f(n)=3f(n-1)+4^n$$
This is a more standard problem now.
Note,
$$4^{n+1}=3(4^{n})+4^n$$
Subtracting this from the previous equation gives,
$$f(n)-4^{n+1}=3(f(n-1)-4^n)$$
$$g(n)=3g(n-1)$$
With $g(n)=f(n)-4^{n+1}$.
So,
$$g(n)=g(0)3^n$$
Now we unwind our substitutions.  
$$f(n)=g(0)3^n+4^{n+1}$$
$$T(2^n)=g(0)3^n+4^{n+1}$$
We also have $g(0)=f(0)-4=T(1)-4$.
So,
$$T(2^n)=(T(1)-4)3^n+4^{n+1}$$
Or if you wish, with the substitution $n \mapsto \frac{\ln n}{\ln 2}$:
$$T(n)=(T(1)-4)3^{\frac{\ln n}{\ln 2}}+4n^2$$
