The h-index was suggested by physicist Jorge Hirsch to be used as a tool to determine an individual's scientific research output. The index is based on the number of times an author's research has been cited.
An Index to Quantift an Individual's Scientific Research Output (J. E. Hirsch)
"I propose the index h, defined as the number of papers with citation number ≥h, as a useful index to characterize the scientific output of a researcher." This is the paper that started everything.
To calculate an H-index manually, one only needs the total number of papers a researcher has published (Np) and the number of citations (Nc) for each paper. The H-Index is determined "by how many (h) of a researcher’s publications (Np) have at least (h) citations each".
(Image via Benchfly)
Video that explains how to find an H-Index manually, through Scopus, Google Scholar, and Web of Science.
Google Scholar Citation Gadget
"Please note that this tool is as accurate/inaccurate as Google Scholar itself. Thus it is important to check and refine the data that the gadget performs calculations on by clicking on the "view publications" link."