You didn't provide very much info. There are two parts to setting up email normally... Inbound which is typically POP/IMAP and Outbound which is SMTP.
If you are getting mail fine, then you have the POP/IMAP part done right.
If you are not able to send, you need to fix the SMTP part.
Without knowing much more than that, like how you setup your SMTP settings and what Verizon needs to have setup, there is no way to help much. I don't use Verizon for mail services and you didn't say which type of Verizon email you are using (assumption is Wireless, but it could be FIOS or some other service).
Unless you have some sort of error message that provides more detail on what is erroring... it would be hard to say.
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