To delete a family member, you first have to select them.Below the info fenster on the left of your screen are multiple options (i. e. "Add brother/sister", "Add partner/ex"); select "More Actions". This opens a menu with buttons such as (depending on the person marital status, parents etc.) "Set parents", "Change partners" or "Add new friends".
The last button says "Cancel", and above it usually is a button labeled "Delete [first name]". If you click it, you'll have to confirm you want to delete them, and you're done.
There are, however, some people you cannot delete because that would split the tree. If you had a tree with a couple, their son and their grandchildren, you wouldn't be able to delete the grandchildren's father as this would remove the connection between the kids and their grandparents. To delete the father, you'd thus have to delete his children first.
Hope this helps!