If you have permission to update an asset then you will see an 'Edit' button on the Asset details page.
On this page you can change the metadata of the asset, upload a different file for the asset (e.g. replace a document with a new version), and change the categories and folders that the asset resides in.
As with uploading you will have multiple submit options at the bottom of the page; to either submit the changes to live or for approval. If the changes are submitted for approval then other users will not see the new details until an administrator has completed the approval process.
If your Asset Bank has versioning enabled then you may also see an option to save your changes as a new version - this would mean you have the option to revert back to previous versions of the asset or metadata in the future if needed.