First, you’ll need to enable iCloud on your iPhone or just double-check that contacts are already being synced with iCloud. (in your phone settings, click into iCloud and make sure Contacts is enabled)

On your computer, open a new browser page and navigate to icloud.com and log into your iCloud account

Click into the Contacts icon where you should then see all of your contacts from your phone

Click on the first Contact's name and then Ctrl+A which should select ALL contacts

While all contacts are selected, click the gear icon in the lower left side of the page and select Export vCard