To edit a donor’s details, just click on it on the main Donors View.
The dialog that comes up is like this:
On this dialog, all of the donor fields are on the left, and any donations that have been entered for them are on the right. You can make any desired changes to the donor, and click Save at the bottom right to save them, which also closes the dialog.
If you have enabled Pledges on the Organization Preferences page, a pledges section appears below the donations section, as shown above.
If the donor doesn’t have any donations or any receipts, you can delete it, and there will be a red “Delete donor” link at the bottom left of the dialog for doing that. (You can delete a donor that has pledges, as long as they don’t have any donations or receipts - doing so will also automatically delete those pledges.)