Upload in form API

I am developing a custom module and I understand the form API to a degree. I am having trouble with the upload function. I need an upload box to upload a file into a child directory in the files folder. It also needs to validate that the file is a pdf file. I have posted my code below. Hopefully someone can help!

function schematics_perm() {
  return array('access schematics');
}

function schematics_menu() {
  $items = array();
  $items['schematics/form'] = array(
    'title' => t('Insert Schematics into the database'),
    'page callback' => 'schematics_form',
    'access arguments' => array('access schematics'),
    'description' => t('My form'),
    'type' => MENU_CALLBACK,
  );
  return $items;
}

function schematics_form() {
  return drupal_get_form('schematics_my_form');
}

function schematics_my_form($form_state) {
  $form['insert'] = array(
    '#type' => 'fieldset',
    '#title' => t('Insert Schematic Into Database'),
    '#collapsible' => TRUE,
    '#collapsed' => FALSE,
  );
 
  $form['insert']['id'] = array(
    '#type' => 'hidden',
      );
  
   $form['insert']['model'] = array(
    '#type' => 'textfield',
    '#title' => t('Model Number'),
    '#description' => "Please enter the model number of the machine i.e. TTB4552",
    '#size' => 60,
    '#maxlength' => 60,
  );
  
  $form['insert']['description'] = array(
    '#type' => 'textfield',
    '#title' => t('Description'),
    '#description' => "Please enter the description of the schematic i.e. Brush Base Assembly or Vac pod assembly",
    '#size' => 60,
    '#maxlength' => 60,
  );
  
  $form['insert']['min'] = array(
    '#type' => 'textfield',
    '#title' => t('Serial Number Start'),
    '#description' => "Please enter the first 4 digits of the starting serial number",
    '#size' => 60,
    '#maxlength' => 4,
  );
  
  $form['insert']['max'] = array(
    '#type' => 'textfield',
    '#title' => t('Serial Number End'),
    '#description' => "Please enter the first 4 digits of the ending serial number",
    '#size' => 60,
    '#maxlength' => 4,
  );
  
  $form['insert']['schematic'] = array(
    '#type' => 'textfield',
    '#title' => t('Schematic File Name'),
    '#description' => "Please enter the file name of the schematic. This file must be uploaded to the site via FTP in the sites/default/files/schematics folder.",
    '#size' => 60,
    '#maxlength' => 20,
  );
  
   $form['insert']['submit'] = array(
    '#type' => 'submit',
    '#value' => 'Submit',
  );
  
   $form['insert']['clear'] = array(
    '#type' => 'submit',
    '#value' => 'Reset form',
    '#validate' => array('schematics_my_form_clear'),
  );

  return $form;
}

function schematics_my_form_clear($form, &$form_state) {
    $form_state['rebuild'] = TRUE;
}

function schematics_my_form_validate($form, &$form_state) {
    $model = $form_state['values']['model'];
    $min = $form_state['values']['min'];
	$max = $form_state['values']['max'];
    $schematic = $form_state['values']['schematic'];
    
    if (!$model) {
        form_set_error('model', 'Please enter a model number');
    }
    if (!$min) {
        form_set_error('min', 'Please enter a starting serial number.');
    }
    if (!$max) {
        form_set_error('max', 'Please Enter a starting serial number.');
    }
	if (!$schematic) {
        form_set_error('schematic', 'Please Enter the file name including the file extension i.e. <strong>schematic.pdf</strong>.');
    }
}

function schematics_my_form_submit($form, &$form_state) {
db_query("INSERT INTO schematics (id, model, description, min, max, schematic) VALUES ('%s', '%s', '%s', '%s', '%s', '%s')", $form_state['hidden']['id'], $form_state['values']['model'], $form_state['values']['description'], $form_state['values']['min'],  $form_state['values']['max'],  $form_state['values']['schematic']);
    drupal_set_message(t('The form has been submitted.'));
}