The Media Library is accessed on the Dashboard toolbar on the left side menu. Just click on the "Media" section and you'll be taken to the Media Library. From here, you can view all current media added to your site, add new media, and edit and/or delete current media as necessary.
To add a new item, you can click on "Add New" towards the top of the screen (directly after "Media Library" text) or you can simply drag the media itself from a folder on your computer into the main part of the media library view. The item will then be uploaded an you will be free to link to it as you wish.
If you click on an uploaded media item, you will be presented with additional items that can be edited for that particular item (see screenshot on left). It is important to add a descriptive title which should also go in the "Alt Text" section. That is where screen readers will get the text for that particular item if it is not readable for visually impaired visitors to your site. If you would like a caption to be included below the item when you place it on your page, add to the "Caption" field as appropriate.
For more detailed information on the Media Library, please see the Media Library Screen page on the WordPress.org Codex.