Go to Settings > Mail, Contacts, Calendar > Accounts and set up your Yahoo account. If you don't want to use the Mail or Calendar app syncing, turn them off. Your contacts will show up in the Contacts app.
Yahoo does not support contacts in the mobile version of it's webmail. While you can get around this with some third party browses by going to the desktop site, that site does not work well with mobile devices. Google is no better at this, for what it is worth.