Documentation on this topic is still a bit low but it's not that complicated.
First, create a new TYPO3 extension that will be a container for an Aimeos extension and the rest of your changes or additions you would like to make: http://docs.aimeos.org/TYPO3/Extend_Aimeos
Then you should go to the typo3conf/ext/aimeos/vendor/arcavias/arcavias-core directory and execute "phing createext". Make sure you have the phing command installed (phing.info). Enter the name of your project and after the extension was created, move it to your new TYPO3 extension in the Resourced/Public/Ext directory like described in the docs. AFTER you've adapted the TYPO3 extension according to the docs, install it in the extension manager. Now you are ready to overwrite templates or create new ones.
The templates can be found in aimeos/vendor/arcavias/arcavias-core/client/html/layouts/. If your layout isn't possible by overwriting the CSS, you can copy the template in layouts/ to the same location in your Aimeos extension (<yourtypo3ext>/Resources/Public/Ext/<extname>/client/html/layouts/...). This template will now be used instead of the original one.
Creating a new subpart additionally requires a class in the src/ directory structure. This is most often a copy/paste and find/replace thing. New data can be assigned in the _setViewParams() method.