It starts with the project sponsor -- this is the one individual who should have an initial vision for the project and know who is involved and what they might need to know.
The project team, as they work with the project manager on the planning will also have some input. As you create the WBS, some additional stakeholders may become known.
Finally, some of them will find you -- perhaps in unexpected ways. One project I worked on was essentially delayed because of a politician with a special interest had not been consulted. While the project charter was amended to meet the needs of this individual, six months passed. Once again, this highlights a need for the project sponsor to have some of this knowledge early or the charter won't even get off the ground.
Once you have identified the stakeholders, you will need to discuss expectations with the sponsor, the project team, and the stakeholders. To confirm the needs, the best approach would be to generate a project communication plan outlining who the stakeholders are, their individual information needs, the messaging they should receive, as well as the frequency and media for communications. This plan needs to be circulated to the project team and stakeholders for review and feedback.