The idea is to add a transparent textarea over the Grid when the widget is focused. The user will actually paste inside the textarea without knowing that. When something is pasted, it will be your task to parse the pasted content and populate the Grid via its dataSource API. When the user focuses something else on the page, the textarea should be removed.
The above example expects the pasted content to match the order and number of the grid columns. You can use any other custom logic, which will suit your users' behavior, but in the standard case, you will need to require the pasted data to be in a certain format and/or meet some other requirements.
In order to enhance the above example, you will need to be familiar with Grid and Grid DataSource API methods.