Most databases will allow you to save your searches and set up a variety of RSS feeds or email alerts. The process varies with each database.
You will generally need to create an account. Look for links such as Sign In, Log In, Register or anything starting with My... e.g. My Tools, My Account, My Projects etc.
The option to save a search and set up alerts for new results is usually offered after you have conducted a search. On the results screen look for phrases like Create an Alert, Search Alert, Save Search or symbols such as for saving, for email or for RSS feeds.
To set up table of contents alerts you often need to find the record for the journal first. You can usually browse journal titles by subject or alphabetically. Look for tabs or pages such as Browse, Publication List, Title List or Journals. If you know the name of a journal you may be able to search Journal or Source Titles. Once you've found your journal record look for an RSS symbol or words like Create Alert, Content Alert, Publication Alert, TOC Alert. Some databases enable you to subscribe to a journal table of contents alert from article records. If available this functionality is usually more fully described, for example "Create TOC alert for this journal".
Some databases offer citation alerts although this is not as common as search or table of contents alerts. Find the record for the article you wish to create an alert for. Look for terms such as Citation Alert or Track Citation in either the article record or the full text.
You can generally manage your alerts from your account area within the database. Email alerts will often provide a link and instructions on how to modify or delete an alert. RSS feeds can be deleted from your RSS reader.
All databases have a help page. These often contain a section on setting up alerts and advertise what functionality is available. You may also be able to search a FAQ page for further help.
Note that the alerts in each database will only return results from that particular database. For example, if you set an author alert in Scopus and that author publishes an article in a journal not indexed in Scopus it will not appear in your author alerts.