I myself am a transgender guy, meaning I was born female, so I hope I can help you a bit with this.
Before I start I'd just like to say that I'll be using gender-neutral pronouns in reference to your partner (they/them/theirs). I also would like to say that your reaction is good that you're looking for information and help.
First you need to ask them if there is anything you can do to help, and if you can't do those things, talk to them and explain your stance. If you can no longer be in a romantic or sexual relationship with them, discuss that too. Also know that the fact that they have told you says that they trust you and care for your help and support.
Secondly, while you are correct about needing some form of "counselling", this is purely for medical treatments. I have been living socially as male for almost a year now, but only started hormone treatments a week ago. It takes a few appointments with 2 different psychiatrists to start any form of medical treatment, but because of the limited services available, it take about a year for this process to be completed.
In terms of supporting them as a friend, it may be good to look up more about what its like to be transgender (I can link you some YouTube videos if you want) so that they feel like they can have open conversations about it.
Two things that are probably the most important: mental health and violence. While I myself haven't experienced any physical violence based on the fact that I am trans, most trans people will experience a very negative attitude towards them. This can be physical or verbal in nature, and can also end in murder. Mental health is a huge factor. If your partner has/had any mental health problem (depression in particular) then I suggest looking up ways to help them with their mental illness. I'm going to give you a statistic that may be scary, but it will put things in to perspective: 41% of transgender people have attempted suicide in their lives. Make sure that your partner has someone that cares for them, and reach out if you believe they are in danger.
If you need any more advice or information, please don't hesitate to get in touch with me. (I am more active on twitter too: @bobertie10). I hope that everything goes well and that you both find the peace you deserve.