Step 1: Find how many electrons copper has.
Copper has atomic number $Z=29$, so a neutral copper atom holds $29$ electrons. To write its configuration we must arrange these $29$ electrons into shells and subshells.
Step 2: Use argon as a shortcut.
The nearest noble gas before copper is argon, which accounts for the first $18$ electrons. So we write $[\mathrm{Ar}]$ and only need to place the remaining $29-18=11$ electrons.
Step 3: Fill in the expected way.
Following the normal filling order, the $4s$ fills before $3d$. The simple expectation would be $[\mathrm{Ar}]\,4s^2\,3d^9$, using $2+9=11$ electrons.
Step 4: Apply the stability rule.
A fully filled $d$ subshell ($d^{10}$) is extra stable because the electrons are spread out very evenly. Copper grabs this stability by shifting one electron.
Step 5: Move one electron.
One electron jumps from $4s$ into $3d$. \[ [\mathrm{Ar}]\,4s^2\,3d^9\;\longrightarrow\;[\mathrm{Ar}]\,4s^1\,3d^{10} \] Now $3d$ is full and the atom is more stable.
Step 6: Pick the matching option.
The real configuration of copper is $[\mathrm{Ar}]\,4s^1\,3d^{10}$, which is option 1. \[ \boxed{[\mathrm{Ar}]\,4s^1\,3d^{10}} \]