I would add to this discussion that a short written letter (you keep a copy) that says the attorney-client relationship is terminated might be useful later. Why? It is a written termination record should a dispute arise about when legal work was done and on what issues.
There's no official process for firing your lawyer. You can simply send a letter notifying them. However, it's often a good idea to find a new lawyer first. Not only will they help you end things with your current lawyer, but there won't be any gaps in your case while you find someone new. You don't say why things aren't working with your current attorney, but make sure to do your research before choosing who should take over your case. Ask a lot of questions upfront to avoid misunderstandings later. And if it doesn't feel right, keep looking. There are more tips in the link below. If you have other questions or need a referral, feel free to give me a call. 1-800-517-1614.