If 50% of the league (outside of the two involved teams) says no to a trade, it will be automatically vetoed. That number can be adjusted by LM in private leagues. 

Veto trade via web
Veto trade via fantasy app

To veto a trade via Web:

Once a trade is accepted, every manager will receive an email with the trade details. 

Title of the email: A Trade in Your ESPN Fantasy Baseball League Has Been Accepted 

You will need to click "Vote on trade" and click "Vote"

You can then elect to allow or VETO a trade.

To veto a trade via Fantasy App:

Once/If you receive an email regarding an accepted trade, you can click "Vote on Trade" on the email. It should bring you to the fantasy app. If not, you can manually visit the fantasy app as well. 

Under League -> Recent Activity

Locate the accepted trade, click "Vote On Trade"

You can then "Vote to Veto" or "Vote to Uphold"