If you're still a student, a great way to get to know them is to attend the various events they organize. Many of the thinktanks I've been involved in hold events that allow students to attend for free, or at a really low cost. It's great networking (everyone else is paying quite a bit to be there) and you get to know the thinktank staff as well.

Volunteering could also be a good way to do things. Many of the people I know in political parties, NGOs, etc. know people working in thinktanks as well.