If you created a website for your research project you can collect statistics about who is using it. Google Analytics is a free platform that keeps track of this information and provides reports that include information such as which state/country your users are from and which pages/items are being clicked and used.
If you don't want to use Google Analytics there are other programs available. If you are using a service like WordPress, they may already collect this information for you.
You can gather altmetrics through social interactions online. Not all platforms are open, but some have open APIs that allow other websites to harvest statistics. Retweets, likes/favorites, and shares are a way to track the interest level of a research project or article. Comments on blogs, reviews, articles, etc. are another place you can look.
Reference management tools offer another source of altmetrics. There's been some research that shows that the number of times an article is "saved" by users may correlate to later citations.
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.
The following list, by no means exhaustive, shares some publicly visible examples. Other publishers may provide authors with statistics but do not make them publicly accessible.
* Taylor and Francis metrics example
Many digital repositories provide authors with a dashboard that show statistics about their works in the repository. These statistics are separate from the statistics gathered by publishers, so archiving your work in a digital repository could provide you additional metrics to take into account.