Remote Desktop.. Well - there is "shadowing" - but that is not meant for the
Remote Assistance is what you are looking for. Check into that instead.
(It will require that the person at the other end invite you, you accept and
use the invitation, they allow you onto their computer and if you want to
control it - you take control and they allow that as well.)
Otherwise.. TightVNC or UltraVNC are your freebie friends.