Don't panic. Whenever I go to therapy I always plan what I'll say but it's never how it really works out. Just be yourself. The goal is you feel comfortable enough to talk to them about anything. Give it a few sessions, so if it's still weird, ask for a new counsellor.
Just let them lead if you're not ready to talk. It's your space to say/do whatever you want without judgement, so that's all that matters. Cry, yell, whatever, just make it clear to them how you feel. If you're not honest to them, truly honest, whether you don't think you should be there, or whether you think everything is your dog's fault BE HONEST. They won't judge and won't tell anyone anything unless they think you're in danger, and they will ask you first. So don't worry! Just do or say what you want, since people rarely get that chance these days.