The default "links" block (called "View: Links" on the blocks page) on a public site is a "smart block" so it's content is not directly editable, and instead displays content that ahs been added separately.
To add a link
Go to: Add content > Links
Add a title for internal use - this can describe the link so when editing, you know which one it is.
The second title field is the text that the visitor will see when viewing the link in the Links block. Sometimes this is more instructional.
So your internal title might be "facebook", and your second external title might be "Follow us on facebook!"
The URL field is where you'll add the url link you want them to click on.
Links will appear in the order they've been added into the system, but the Order field will allow you to choose the order of the links. 1 is first. 5 is last, etc. Negative numbers should not be used.
When you're done, remember to save.
To edit or remove links from this block:
Go to: Settings & admin > content
Filter for type = Links
This will show a list of all the current links content. You can edit the links by clicking on their titles, or using the options to the right of their name.