Some publishers provide altmetrics on their websites to authors and the public. Many large publishers are now collecting usage data or are partnering with other companies to provide this information to their users. PLOS has been a leader in providing altmetrics to both readers and authors. Each article they publish has a "Metrics" section which provides a wealth of information. Click the image below to see an example.
Many digital repositories such as Iowa State's Digital Repository @ Iowa State University (DR@ISU) provide authors with a dashboard (example below) that show statistics about their works in the repository. These statistics are separate from the statistics gathered by publishers* so if you are archiving your work in a digital repository make sure you take these into account! DR@ISU does display the Altmetrics badge for journal articles but it does not include downloads made through the repository.
Click the image above to see an example of an Author Dashboard.
There are many different ways to share and store your research with the world. Some services are better than others for the purpose of gathering altmetrics. Look for services that use an open API, partner with a company such as Altmetic, or provide usage statistics. For a comprehensive list of tools that can be used throughout the research process, visit 101 Innovations in Scholarly Communication.
This list shares some examples and is by no means exhaustive. Some publishers may provide authors with statistics but do not make them publicly accessible (which is great for authors but doesn't help anyone else).
DR@ISU provides two different altmetrics
Altmetric - the company - provides ISU with free non-commercial use of the badge on DR@ISU.