I been having problems with my Mail client on my iMac with Mavericks. How of I add an alternative web based email to my Mail client, please?

Open the Mail app.

From the Mail menu bar click Mail > Preferences then select the Accounts tab then the Account Information tab.

Click ➕ under the panel on the left then follow the instructions.

Further help here > Mail settings you might need from your email provider

That's a bit unclear but it seems that you want to stop using the mail client and start using the web interface, is that correct?