Only communicate with clients through Upwork messages, using any other communication method violates the Upwork terms of service. You are also more likely to be scammed if you take your clients outside of Upwork. That's why Upwork encourages you not to do so.
As Sohail mentioned, It's against our TOS to share your contact information or to ask others to share theirs before a contract starts. We provide secure tools for you to communicate directly from the Upwork platform. Once a contract is in place, you can choose to share your contact information and use other tools to manage your project, too.
Let's hear what other members get to share here on this thread for the best way/tools of communicating with clients.