How do you fire a client?

This question is all wrong. You don't fire a client. You bill them. Any well written work agreement should take care of the project scope and how much is paid per billable hour for additional changes that are outside of scope. I simply tell the client when they are adding features that are out of scope, configure an estimated time for additional work that they are asking for and send them an addendum for the original contract. 99% of clients have no issue with this and either accept the addendum or curb their wants. Often time I can use this to make recommendations to the client for features they may wish to add to their project in "phase 2" after they have some ROI.

The phrase 'I'm pursuing bigger contracts' tends to work pretty well. No need to get all lengthy and dramatic about it.

I think the best approach is to be honest, say that you don't think the project is working out. Make a clear ending point for the work that is currently in progress and then help the client transition to a new team.

Raise your salary. I'm sure that you'd like to continue struggling with this particular client if only he payed you lots more of money. So, ask him/her that. IMHO, my clients don't have to run my business, I run it. And I do it with my conditions. So, the one who doesn't follow can leave or pay an extra fee to be allowed to disturb me.

Communications is the key, if you really want to stop the project, then you must have a good and clear reason about that and know the consequence. If you still work with them and they just need to appreciate you more in term of package or your work, just talk with them. Sometimes they just forget how to appreciate us because they are too busy or stress too.

Anon because I have clients on Quora! =D Firing is (almost) never necessary.  It is an unnecessary emotional milestone that leaves you looking like the antagonist.  You simply need to wrap things up with this batch of changes, have no availability for the foreseeable future and will get back in touch when you do.  Send them a thank-you card (or similar appropriate gift) thanking them for working with you.

Prepare in detail the reasons for terminating the relationship. On the basis of your question, I assume that beyond the specific project you do not wish to work with this client anymore. However, you do want a clean break, so outline the process for the client about how you will hand over the project to someone else (of their choosing). If you can and want to (depending on the specifics of your relationship with the client) you may want to suggest some people/companies that may be better suited to finish the project. Make it clear, though, that you are NOT looking for more money, but rather, that the scope of the project has grown too big for you to manage, you recognize that you cannot provide them with the most appropriate solution to their wants/needs. Otherwise you risk getting dragged into a conversation about price, which is what you are trying to avoid.

Now a days, you want to let people off easy - especially those that you've given access to your website. You don't want ANYTHING shady to happen. But sometimes you just have to be blunt. Write your termination letter/email and give them reasons why you have to let them go. If you need help creating a termination letter you can check out the template on this site: http://wheniwork.com/hr Most people will appreciate constructive feedback if you tell them how they can improve in their next endeavor.

I think Don on MadMen fired a client the best way i've seen in a while.  they also fired a member of staff this way... Nice restaurant, dinner and drinks, and an honest conversation.  Ah the good old days.