Citations to publications are the most common indicators of impact.
You can find citation counts, how often an article was cited in other scholarly works, on websites such as Google Scholar or databases such as Web of Science or Scopus. These counts are collected at the level of an individual publication (article-level indicators) and can be "rolled up" to include all publications by an individual author, research group, institution or country. H-Index is an example of an indicator derived from calculating citation counts to a group of publications (traditionally, of an individual author, but also research groups or entire institutions). Indicators constructed using aggregate citation counts to groups of publications can be also used to measure impact of journal titles (Clarivate Analytics' Journal Impact Factor (JIF) is one such example).
Alternative metrics or altmetrics have potential to show impact of a broader range of research outputs.
While citation counts have been used for some time to assess impact of research, new modes of scholarly communication enabled by new technologies allow now for capturing a greater variety of impacts. Indicators based on measuring and benchmarking usage of scholarly content outside journal article are know collectively as alternative metrics or altmetrics. These metrics have potential to show impact of a broader range of research outputs (citations are usually counted for journal articles) and impact outside the research community.
Web of Science (WoS) is a citation index that provides citation counts to articles in nearly 20,000 peer-reviewed research journals across all disciplines, through its component indices: Science Citation Index (SCI), Social Sciences Citation Index (SSCI) and Art&Humanities Citation Index (A&HCI). University of Pittsburgh subscription allows for searching their content from publications going back to 1945 for SCI and 1992 for SSCI and A&HCI. The newest addition is Emerging Sources Citation Index (ESCI) with content available form 2015, expanding WoS coverage by additional 2,500 titles of regional importance and from emerging disciplines .Conference proceedings and book data are also available.
SCOPUS is another good source of citation data (as well as altmetrics data). It is published by Elsevier and claims to index: over 21,500 peer-reviewed journals, including 3,000 full open titles, over 360 trade publications, over 5,000 articles in press from international publishers, more than 131,000 books, over 520 book series with subject areas focusing on Social Sciences and Arts & Humanities, but also including STM subjects. Also includes conference papers and over 27 million patents.
Google Scholar is a good source of citations. It is especially useful for authors and publications in disciplines less well covered by the commercial services (listed above), but it can inflate citation counts because it indexes varied content, including college reading lists, library bibliographies, etc. An author search in Google Scholar will produce a list of publications with citations as well as link to Google Scholar Profile (if available).