gistfile1.php

<?php

// Get the entry
$entry = craft()->entries->getEntryById(100);

// Define the new Matrix data
$matrixData = array(
    '1' => array(                           // '1' is an existing block ID
        'type' => 'text',                   // 'text' is the block type handle
        'enabled' => true,
        'fields' => array(
            'textField' => 'Lorem ipsum'    // 'textField' is the field handle   
        )
    ),
    'new1' => array(                        // The 'new' prefix tells Matrix this is a new block
        'type' => 'image',                  // 'image' is the block type handle
        'enabled' => true,
        'fields' => array(
            'assetsField' => array(200),    // 200 is an asset ID
            'captionField' => 'Some caption'
        )
    )
);

// Set the new Matrix data
$entry->getContent()->matrixField = $matrixData;

// Save the entry
craft()->entries->saveEntry($entry);


/* NOTE: Craft 1.4 will come with APIs that make it possible to directly edit Matrix field data,
 * without going through the owner element (the entry, in this case).
 *
 * The above will still be possible, with one exception: line 26 would need to be rewritten to:
 *
 * $entry->setContentFromPost(array('matrixField' => $matrixData));
 */

Relationship fields:

// Grab existing relational IDs
$newIds = $entry->myEntriesField->ids();

// Add any new IDs
$newIds[] = $newEntry->id;

// Set them back on the relational field
$entry->myEntriesField = $newIds;

// Go through the entries service to let it save everything.
craft()->entries->saveEntry($entry);

Fetching Matrix fields:

$criteria = craft()->elements->getCriteria(ElementType::MatrixBlock);
$criteria->ownerId = 100; // entry->id
$criteria->fieldId = 5; // matrix field id
$blocks = $criteria->find();