Answer:
Option 1: Tu y yo estamos navegando por el internet.
Translation 1: You and I are surfing the internet.
Option 2. Tu y yo estamos navegando
Translation 2: You and I are browsing
Explanation: I hope this helps you. I personally would go with the second option, but it is up to you. unless the question is about what they are doing on the computer. If this is the case then the first option is best.