You have two options:
The easy way is to install an extension that puts these buttons on your posts. You can search wordpress.com's plug-ins database, here is an example, but there are many more: http://wordpress.org/extend/plugins/really-simple-facebook-twitter-share-buttons/
You can also search for these from within your Wordpress admin interface to install these with one click.
The more complicated, but more customized way is to edit your wordpress template. Usually /wp-content/themes/YOURTHEME/posts.php contains the block you need to edit. Copy the code you need for the buttons (you'll find them on FB's and Twitters dev site) and consult the Wordpress Codex on where you need to paste them.
You'll probably achieve everything you want with the extensions in the former method, but if you'd like the buttons or their placement to match your site's design, you should dwelve into template editing.