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How can I set it to get posts from current category?

Select checkbox on widget's settings called 'Get posts from current category'.

I want to display only the posts in two categories.

You have to write their category's ids -separated with a comma- to 'Categories' textbox.

I don't use Widgets. How can use this widget?

template tag: yg_recentposts( $args ) shortcode: [amrp] with args Original author's website.

.... Image alignment ....

If you need serious customization, please go learn CSS. I will not provide extensive CSS support. (Sorry - there are just far too many variations, and I do all this in my spare time)

The most frequest request I get has to do with aligning the image to the right or left. To get started with customization, create a file called amrp-styles.php (really, any name will do) and upload it to wp-content/mu-plugins (you may need to create this directory).

In that file, paste the following

<?php
/*
    AMRP Styles
*/

add_action('wp_head', 'amrp_styles');
function amrp_styles() {
    ?>
    <style type="text/css">
    .advanced-recent-posts {
        /* remove bullet points */
        list-style-type: none;
    }
    .advanced-recent-posts li {
    }
    .advanced-recent-posts li a {
    }
    .advanced-recent-posts li img {
        float: right; /* change to left if you'd prefer */
        margin: 3px;
    }
    </style>
    <?php
}

Of course, if you have the skills, feel free to relocate that CSS.