Accepted answer

Here is how I do it:

    // Make a post node.                                                         
    $node = new Node();                                                            

    // Use the node type you need here, in this case 'post'.                                               
    $node->type = 'post';
    $node->title = 'Replace This With The Title You Want';                                                          
    node_object_prepare($node);                                                    
    $node->language = LANGUAGE_NONE;                                               
    $node->uid = 1;                                                                
    $node->status = 1;                                                             
    $node->promote = 0;                                                            
    $node->comment = 0;

    // Save your field data.                                                     
    $node->field_author[$node->language][]['value'] = getMetaAndClean($thisBlog[8]);
    $node->field_date[$node->language][]['value'] = getMetaAndClean($thisBlog[13]);
    $node->field_byline[$node->language][]['value'] = getMetaAndClean($thisBlog[12]);

    // Save submit and save the node.
    $node = node_submit($node);                                                    
    node_save($node);

Comments

Here is how I do it:

    // Make a post node.                                                         
    $node = new Node();                                                            

    // Use the node type you need here, in this case 'post'.                                               
    $node->type = 'post';
    $node->title = 'Replace This With The Title You Want';                                                          
    node_object_prepare($node);                                                    
    $node->language = LANGUAGE_NONE;                                               
    $node->uid = 1;                                                                
    $node->status = 1;                                                             
    $node->promote = 0;                                                            
    $node->comment = 0;

    // Save your field data.                                                     
    $node->field_author[$node->language][]['value'] = getMetaAndClean($thisBlog[8]);
    $node->field_date[$node->language][]['value'] = getMetaAndClean($thisBlog[13]);
    $node->field_byline[$node->language][]['value'] = getMetaAndClean($thisBlog[12]);

    // Save submit and save the node.
    $node = node_submit($node);                                                    
    node_save($node);

Body field is missing from example, but pretty straightforward (after banging my head against wall for an hour):

$node->body['und'][]['value'] = 'This is my test content.';

Now, I'm stuck on adding a taxonomy term to the node using default "tags" (standard installation profile). Any help?

I thought this would work, but it does not:

$node->field_animals_tags['und'][]['taxonomy_term']->name = 'Mammals';