In general, you select the person to delete, click on the "Change or Delete" box at the bottom (in the sidebar), then you'll be given a choice to "Change Parents" or "Delete name".
If you don't see the Delete box, it's likely because that person has children associated with them. You'll need to disassociate each child first, either by deleting that child, or by selecting the child and "Change Parents".
The system won't allow you to delete someone from your tree if their deletion would result in a splitting of the tree into two parts. So it's necessary to delete (or disassociate) everyone under the person you want to delete first.