insert

DB::table('テーブル名')->insert(配列データ);

update

DB::table('テーブル名')->where('更新対象を検索')->update(配列データ);

    $params = [
      'id' => $request->id,
      'name' => $request->name,
      'email' => $request->email,
      'age' => $request->age
    ];

delete

# 使い方
DB::table('テーブル名')->where(検索条件)->delete();

# 削除ルーティング
Route::post('/hoge/delete', 'HogeController@delete');

HogeController.php

  public function delete(Request $request){
    $id = $request->delete_id;
    $person = DB::table('people')->where('id', $id);
    $person->delete();
    return redirect('/hello');
  }