When someone requests help, you can see it through the Dashboard, under their profile or other requests for help, or via a notification. Depending on the privacy settings for others, you might not see their personal details but you will see the information most relevant to the help they need.
If they are visible to you, you can see the full details of the request such as names.
And if their details are private to you, you can still click on their family name to view their profile, and see enough details to know if you can help.
When you can help, accepting the request will show a pop-up where you can select the member(s) of your family that will help as well as provide a message if you like. This is sent back to the family asking for a hand so they can review and confirm the help.