Here are some tools for performing the quadratic sieve.
Set an integer $n$ to factor and find $k$ near the square root of n
Find a factor base (primes < B)
This will find only prime $p < 20$ where $n$ is a square modulo $p$.
Manually factor $m$ values of $k^2-n$ starting at the k indicated above
Sieve $m$ values of $k^2-n$ starting at the k indicated above
Don’t forget to double-check your answer!