Hi. My partner (middle-aged trans-man) has just been diagnosed with Autism and I (middle aged non-binary/masc presenting AMB) want to learn how to be a better partner as I feel like at the moment I'm constantly saying the wrong thing when trying to be supportive. HELP!
Hi and welcome to the community! 
The NAS has some advice here that you might find helpful:
NAS - Family relationships - a guide for partners of autistic people
You might also find this book helpful. It aims to help couples like yours (within which one just person is autistic) by improving your mutual understanding and communication. It also includes some exercises that you can complete and discuss, if you like, as part of that process:
Loving Someone with Asperger's Syndrome: Understanding and Connecting with your Partner
A couple of points to mention:
- The latest diagnostic manuals no longer use "Asperger's"; this is now included under autism / Autism Spectrum Disorder.
- Between discussing one scenario and the next, the author frequently switches the gender identity of the autistic party. This was done to avoid reinforcing stereotypes and can require some effort to keep checking, but I do think it's worth it.
You could also consider couples counselling, ideally with a counsellor who has experience in helping autistic people.
Finally - and in a more direct and literal respect - this document from the NAS explains which words and phrases around the subject of autism are preferred, based on research involving autistic people, their families, professionals, and feedback and insights from its supporters and wider work:
