How to ask other researchers to share their datasets?
Email, unless they happen to be at your university.

Just introduce yourself, and the possibility that their data might be useful for advancing your project. Leave open flexibility about the possibility of acknowledgement/authorship (depending on the effort you're asking them to go to), IRB approvals, data sharing agreements, etc.

Be prepared for rejection, but I've had something like a 60% success rate with this approach, and birthed several really productive collaborations.