Hi Katie
Coming out to colleagues is very strongly dependent on your company's culture and the type of work performed in your part of the company. For example, the experience of someone working in healthcare would be quite different from that of someone in an engineering company or a construction company.
If you have an in-house heath service or some similar group which is associated with your company for health reasons, you could start by discussing your situation with them. They, in turn, may then open a door to the HR department, and that should help you drive an appropriate attitude down to the management layer and from there to your colleagues.
Above all, you need to control the process, the message and the timing. For example, even in my very progressive company of 100,000 people, I was the first known person to transition, and they had no processes to support me. I built it on behalf of HR and executed it. You should aim to involve a very small group of sympathetic and supportive senior people to ensure that your direct work colleagues are appropriately involved when you are ready.
When you are ready to come out, keep the message simple, and try to fit into your new gender role as quickly as possible.
It would not hurt to consider exploring other job opportunities as an "insurance policy" before you go to your managers, unless labour and civil law in your country directly prohibit discrimination.
So, as you asked, how did we come out? I started with our in-house medic, who opened the door to the head of HR. Once I had HR support I had a quiet chat with my manager and a few other relevant managers. I had prepared some photos of how I would look as a girl, ready to load onto Linkedin and our internal messaging tools. I agreed the coming out date with my managers, and prepared a short email to the 100 or so people in my work ecosystem. That went out on the Friday and they could go to Linkedin etc. to see how I would look when I arrived at work on the Monday. On the Monday I was mobbed by people who came to wish me good luck. I had no direct negative experiences, though I was aware of a few silly comments which my managers addressed very rapidly.
Hope this helps!
Julia