Go to Web of Science and search for the author by selecting Author from the drop down list.
For best results, add relevant institutional affiliations by clicking "Add Row," then select "Affiliation" from the drop down list. Start to type in the institution, and select from the list of suggestions.
From the results, click "Citation Report"
The resulting page will show high-level data, with an option to export a full report:
You will need to review and exclude any papers that are not actually yours. Scroll down and click the minus sign next to any publications you'd like to remove from the calculation.
Web of Science indexes selected journals, and generally doesn't include things like conference proceedings or book chapters. You may get a different "score" using different data, such as Google Scholar.
Considerations
The H-index provided by Google Scholar may be different than the value provided by Web of Science, because both databases cover different material.
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