First of all, it's normal to be really scared before your first session, but equally there's no reason to be! You will probably be surprised at how much kinder to you the counsellor is than you are to yourself.
Your counsellor will start you off and your first sessions will be simply about identifying issues and discussing some of the basics. Don't expect any huge revelations or for it to work miracles overnight. It takes time. It's a process, not a goal. On the other hand, many people start to feel a bit better after just a small number of sessions (two or three).
In terms of the longer process, the most important piece of advice I have for anyone going for the first time is: tell the truth as much as you can right from the start. The more honest you can be, the less you allow yourself to fall into the old ready-made narratives that we all use, the more transformative it will be. We all tell stories to ourselves to excuse ourselves, to mitigate behaviours, to blame ourselves, to act out inner feelings of worthlessness. The ability to recognise and avoid this is one of the most liberating things that counselling can bring.
The second most important piece of advice I have is: listen really, really carefully to what your partner says, what they imply, and also what they don't say. (The counsellor should help you both to do this).
It's vital that you like and trust your counsellor, so if they are not the right person for you, change. However, there should also be room in the relationship for him or her to tell you things you don't want to hear. (This tends to happen much, much later in the process than the first few sessions!) Being open to that is difficult, and takes big courage.
Don't be scared by how deep some of your feelings are, and conversely by how some things you thought really mattered in fact don't. The thing about counselling is that it's a safe place to experience those surprises.
Do expect things to bubble up from the past - things that you didn't even realise you've forgotten.
Don't think that the counselling process ends with the session: tiny, sometimes imperceptible things will trigger awarenesses and learnings outside too. I once had a revelation over a pack of Maryland cookies in Tescos 
Do expect to find it releasing, challenging, tiring, uplifting, and liberating (but not all at once).