I've had this client for a couple of months (2 months to be precise) and this particular client wants it all. I have 'endured' 2 months of 3 different designs and multiple flash animations on the said website. Now my client wants a 4th design and i think i am tired of this client.

At this point, there is no more gain from this project, rather am spending funds on all the expenses; internet bills, power supply, trans, phone calls,

I made a mistake at the begining of the project by not having the client to sign a Terms  and agreement binding the client from making changes on the design.

How best can i fire this client?

Pretty simple, IMHO.  Did you get paid a deposit? If yes, give it back then write him/her thus (I also assume that in one way or the other, you have lodged a (professional) complaint with him/her):

Dear Sir/Madam,

It has been a pleasure and an honor working with you over the past 2 months.

Unfortunately, I am afraid our business relationship can not proceed beyond where it is now.  It seems we can not reach an agreement as to the direction your website should go.  As a sign of good faith, I am also refunding the deposit that you paid me.

Once again, it has been a pleasure and an honor working for you.  Should you need any referrals with respect to another web developer, I will be glad to provide them to you.  I also hope that this issue doesn't mar any possibilities of us working in the nearest future.

Sincerely,

(your name here)

After receiving this letter, I can bet you your next pay check that the person will be standing with their mouth agape, assuming a deposit was made and you have refunded it in full

Lesson:
1) Sign a terms and agreement
2) Be professional, irrespective of client's attitude.  Remember, they pay your bills and you never how who he/she will go bad-mouthing you to.

good luck!

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k yawa, now i'm pissed. you wrote everything i wanted to say
Next time check to make sure I am not about to reply before replying, capish?

@Yawa and Dual Core, thanx for replying.

Yes, i got paid 50% of the project costing with which i have used part of it to registered the domain name and for hosting. Do i refund in full?

Refund in full and tell the client he can get the domain's transfer auth code on request if he wants.

The more sensible thing to do will be to refund in part then keep the money for the domain and hosting. But if you really wonno wash your hands clean clear, refund every and also show readiness to surrender domain name.

@Dual Core, Thanks. I think i'll make it simple.

Dual: u funny o

HC:
Yep, even if it means borrowing from someone, pay in full. Just tell him that you are refunding in full, including domain registration and hosting so he is aware that you are losing money by so doing.

Again he will b amazed that a Nigerian would do such a thing and I bet you, he will have big time respect for you and might even seek to continue the relationship (in which case, you immediately come up with a terms and conditions document )

good luck!

Time to test your host company's money-back policy (if any) 

Interesting issue. A refund would do just fine. However, add the lessons learned to your portfolio as they will help you to deal with other clients in future.

These days, less than 10 minutes with a client tells me if I should reject or accept a project. Time is money and even if you need to do a refund you still get to lose the time you may have spent.

Thanx all for your inputs. I'll go for the refund, even though am giving my client a last chance to make amends.\

Lesson Learned.

lol, i know those kind of clients, they will just move on.

a full refund will be better.
but they have to buy the domain and hosting back.

you can spend that much time and still be at a loss, well u are already anyway.