Simplest way to achieve this might be to just add a hidden input to your product/view.phtml (inside the #product-addtocart-form), like
<input type="hidden" name="related_product" value="17,133,87"/>
... where 17,133,87 is a comma-separated list of the product ID's to add.
Basically, looking at the code in CartController::addAction(), it all comes down to using the Mage::getSingleton('checkout/cart')->addProductsByIds($arrayofproductids) method you could of course apply almost anywhere in code
+++ edited for improved flexibility +++
However if you need to apply any further logic on which products to add additionally or want to change the quantities you will have to set up a custom module with an event observer listening to checkout_cart_product_add_after event. You will find loads of hints how to do this on google.
In your event observer method you can best use
$product = Mage::getModel('catalog/product')->load($productid);
Mage::getSingleton('checkout/session')->getQuote()->addProduct($product, $qty);
hope this helps ;)