How set up Messages in El Capitan?

I'm not sure what you mean by "monitor messages," but Messages on Mac and Messages on your iPhone are designed to mirror each other. On your iPhone, make sure you have iMessage enabled in Settings > Messages > iMessage.

Do you not see this in Messages > Preferences > Accounts?

Make sure both your iPhone and you Mac are using the same Apple ID. This may help:

Add or remove your phone number to iMessage or FaceTime on your Mac, iPad, and iPod touch - Apple Support

If you are using Messages without an iPhone, you can only add accounts by email.

Messages can be used with multiple types of email accounts, including Yahoo and Google.

Open Messages, then click Messages > Add Account

If you already have an account added to the computer, there are two ways to check if it can use Messages:

1.  > System Preferences > Internet Accounts > (Click on your account) > Tick the box for Messages, if your email supports Messages

2. In Messages, click Messages > Preferences > Accounts > Click your account > Tick the box to "Enable this account"

Which email providers are you using? Have you tried adding one of your emails straight into Messages in Messages > Add Account?

You could try removing the accounts and then add them again. If the option was there and is now gone, try booting into Safe Mode and see if the option reappears. If it doesn't then there could be an issue with the OS, perhaps a bad download of El Capitan.

You could boot to the Recovery drive and run First Aid on your hard drive to make sure there are no errors. If you do all of this and it still does not work, then you most likely need to reinstall Messages, which means reinstalling El Capitan.

Best of luck

Good to know! Glad I could point you in the right direction.