This process can be done by going to your "My Account" page from the dropbox under your username or from the tournament page you wish to enter when it asks you to "Add Game ID" then follow the steps. 

Tournament Page - 

My Account - 

Step 1

1.Sign into steamcommunity.com or via your Steam Program
2. Go to Edit Profile
3. Go to My Privacy Settings
4.Set "Profile Status" to "Public

Step 2 

Expose Public Match Data

1.Start Dota 2
2.Open Settings
3. Switch to Tab "Options" and select "To Advanced Options"
4. Check "Expose Public Match Data"

Step 3 

A Click box will appear saying

1. Sign in through Steam