Thought on sharing this, as it is a little bit hidden on :))
Please not, that this will remove the "New" button, but it will not remove underlying functionality. If you want to remove overall new record creation functionality, you will need to update Profile itself, by removing related permissions to the object.
To remove the "New" button please go to 'Setup' and find an object for your page layout. Select 'Page Layout' option.
Click 'Edit' next to the Page Layout where you want to remove the 'New' button from.
Scroll down to Related lists, and click on the wrech icon.
Click on the '+' icon and deselect the 'New' checkbox.
Please make sure that other Page Layouts are not selected in Column section, as otherwise this change will apply to all page layouts. Unless, this is what you want. :)
When done, please make sure to save changes to your page layout.