The procedures will vary depending on where you live. Each state/province/country has its own rules. So you will need to find out locally for your own area what the procedures are, i.e. what forms to fill in, who to contact, etc.
In general you would start with a legal name change. This might be a bureaucratic thing, just filling in forms, or it might involve an appearance before a judge.
Once you have the legal name change, then you have to contact each place where you have an account to change your name separately. The legal name change document does not automatically update anyone else's records. What it does is give you the evidence you need to make the change.
Some places, like online stores, discussion forums, social media, etc, will not require documentation. So you can change your name in those places before you have your legal name change. Other places, such as banks, driver's license, tax office, etc. will require a copy of your legal name change.
The place to start is to research your own state's rules for a name change. Most places nowadays have this information online, so Google is your friend in this.
You should also contact LGBT or trans groups in your area, because people there will already know what your local procedures are.
