In Web of Science, you can collect citation counts in two ways:
Citation counts are displayed for each article listing. Click on the Cited by link to view a list of citing sources.
Keep track of new citations to your work -- sign up for a Google Scholar Author Profile and create an email alert for new citations.
Some subject databases also track citing articles. These databases can be used to augment Web of Science or Google Scholar in some fields. Remember to remove duplicates if using multiple sources to find citations.