Firstly, let's locate and look at your mailserver log. Where are you sending from? If it's a cPanel server, head over to the WHM interface, click the Email button, then choose Mail Queue Manager. If you can locate your message in this list, it means Yahoo! has not accepted it. You can use the 'View Message' button in the Actions column to view the error message that Yahoo! have provided.
Error: "All messages from x.x.x.x permanently deferred" when sending email to Yahoo
This is what we're expecting to see, where x.x.x.x is your sending IP address. If you do see a message like this, please have a look at Yahoo!'s helpful SMTP error code table to understand exactly why they are deferring your message: https://help.yahoo.com/kb/postmaster/smtp-error-code-table-sln23996.html
Once you know the reason for your block and you've remedied the situation, you'll need to fill out Yahoo!'s Bulk Sender Form to request removal. Yes, this applies to everybody, even if you are not a bulk sender and your emails are simply transactional. Make sure you fill in all the boxes, and if they do not particulary apply to you enter N/A or non-bulk sender, something along those lines. You'll find the form at http://help.yahoo.com/l/us/yahoo/mail/postmaster/bulkv2.html
And now, we wait. Yahoo! quote 48 hours to receive a response however in our experience this is more likely to be 7 days or so. Fingers crossed for a good outcome!