To export publications from within Web of Science to Publons, simply search for your publications using the Basic Search in Web of Science.
After typing in your search query, if there are results found, you will be directed to a page where you will be able to select publications to 'Claim on Publons - track citations'. You can either select these publications individually, by adding them to a 'Marked List', or you can import by a range of results.
Please note that after confirming you are the author of these publications, a pop-up will appear to further confirm if you wish to add these publications to Publons. If you have a pop-up blocker extension enabled in your browser, you'll be able to see an icon that this pop-up has been blocked in the right-hand side of your browser's address bar. You can either disable the pop-up blocker on this page, or you can click on the icon and then on the link within that icon to get to the page to confirm you wish to add these publications.
After clicking 'Begin Import', once the import process is complete, you'll be re-directed to your Publications page on Publons where you can view your newly imported publications.