This how to generate citation reports tutorial includes how to:
If you have a small number of citations (or who are regularly the first author on a paper), visually scan the results list and delete self-citations. Those who have a longer scholarly record or are not the first author (such as papers first-authored by graduate students) will find it a bit more difficult to eliminate self-citations.
Within Web of Science, you can add a few steps to your search and have the software eliminate self-citations from your search for you. Tip sheets are on the left side of this page.