H-index is the primary author-level metric that is designed to measure research quality over time.
The h-index is calculated as follows - H stands for the number of articles that have each been cited H number of times.
So, an h-index of 30 means that the author has published 30 articles that have each been cited 30+ times.
To find an author's H-index in Web of Science, first you must find their author profile. This can be quickly done by searching for any article they have published and clicking on their author link. This will pull up a search with all of their articles, with a "Create Citation Link", as shown below.
This citation report will pull together various statistics related to these citations, including the H-index, as shown below.
In Scopus, an author search is generally the best way to pull up citations - search by last name and first initial and institution, if possible (the institution field is useful when you only want to retrieve citations created while at one institution). Choose the appropriate authors listed, then click on "Citation Overview" as shown below.
In the citation overview, the h-index will be listed in a box on the right-hand side, with a link to the h-index graph, as shown below. This better illustrates how the h-index was calculated based on the citation counts for each of the author's articles.
Google Scholar calculates not only h-index, but the i10-index for authors with a public profile which must created by the author.
The i10-index is simply the number of articles with at least 10 citations.
In Google Scholar, searching for an author will pull up the profile as the first result if they have a Google Scholar profile. Clicking on the profile will bring you to their profile page, which includes both metrics, as seen below.