Here's an example install script, in good old DOS batch language. This could probably be easily tweaked to run in PowerShell if you're into that.
This script works with 10.2.x or later (edit for the version you are installing)
For more information about how silent installs work, msiexec options, etc., see the deployment guides referenced in Enterprise Deployment Resources
:: install_arcmap.bat
@echo off
:: Check for administrative access
net session >nul 2>&1
echo.
if %errorLevel% == 0 (
echo Administrative permissions confirmed.
) else (
echo Current permissions inadequate
echo ArcGIS Desktop install failed
goto :eof
)
setlocal
:: Source media folder
:: This folder expected to contain:
:: Desktop\SetupFiles
:: BackgroundGP\SetupFiles
:: DataInterop\SetupFiles
set src=G:\Installs\ArcGIS_107
:: Set the value below to major version
set ARCVER=10.7
:: Install folder (must be a "letter-drive" path)
:: default is C:\Program Files(x86), etc., C:\ArcGIS is easier to manage
set INSTALLPATH=C:\ArcGIS
set INSTALLDRIVE=C:
:: Set log file path, prefix at install script runtime
:: Example logfile name: "ArcInstall_20120925_1623_Desktop.txt"
set DATESTAMP=%DATE:~10,4%%DATE:~4,2%%DATE:~7,2%
set TIMESTAMP=%TIME:~,2%%TIME:~3,2%
set TIMESTAMP=%TIMESTAMP: =0%
set LOG_PATH=%TEMP%\ArcInstall_%DATESTAMP%_%TIMESTAMP%
set MSIEXEC=%WINDIR%\system32\msiexec.exe
set REG=%WINDIR%\system32\reg.exe
@echo on
:: Install