You have two options, you can either extend or overwrite the existing XML.
Extending
To extend an existing layout in a similar fashion to local.xml in Magento 1 you need to add an XML file in a location like this:
<theme_dir>
|__/<Namespace>_<Module>
|__/layout
|--<layout1>.xml
|--<layout2>.xml
Where <layout1>
and <layout2>
are your layout handles, for example:
<your_theme_dir>/Magento_Catalog/layout/catalog_product_view.xml
Official documentation can be found here - http://devdocs.magento.com/guides/v2.0/frontend-dev-guide/layouts/layout-extend.html
Overwriting
Overwriting XML is done in the same way, it's just the file location that changes. You can overwrite the base module's XML or the parent theme's XML, the file location determines which is overwritten.
To overwrite the base module's XML place your XML file in:
<theme_dir>
|__/<Namespace_Module>
|__/layout
|__/override
|__/base
|--<layout1>.xml
|--<layout2>.xml
To overwrite the parent theme's XML place your XML file in:
<theme_dir>
|__/<Namespace_Module>
|__/layout
|__/override
|__/theme
|__/<Parent_Vendor>
|__/<parent_theme>
|--<layout1>.xml
|--<layout2>.xml
Official documentation can be seen here - http://devdocs.magento.com/guides/v2.0/frontend-dev-guide/layouts/layout-override.html