This is a basic script that loads the powershell cmdlets for SharePoint and then creates a MySite if not exist for the user defined in $user

CreateUserMySite.ps1

if ( (Get-PSSnapin -Name Microsoft.SharePoint.PowerShell -ErrorAction SilentlyContinue) -eq $null ) {
    Add-PSSnapin Microsoft.SharePoint.PowerShell
}

$user = "mkunze"

$site = get-spsite("https://domain.com/mysites")

$context = [Microsoft.Office.Server.ServerContext]::GetContext($site)
$upm = New-Object Microsoft.Office.Server.UserProfiles.UserProfileManager($context)

$profile = $upm.GetUserProfile($user)

if($profile.PersonalSite -eq $Null) {
    $DisplayName = $profile.DisplayName
    write-host "Creating personal site for $DisplayName, it doesnt exist yet"

    $profile.CreatePersonalSite()
}