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 now allow for capturing a greater variety of impacts. Indicators based on measuring and benchmarking usage of scholarly content outside journal articles are known collectively as alternative metrics or altmetrics. These metrics have potential to show impact of a broader range of research outputs 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.
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).