I knew about blogger and live journal but they do not let choose my own domain name. How to best host Wordpress on a with free domain? Any experience, feedback welcome

Are you by any chance linking your own site It is always a good idea to list multiple resources when doing that
But it is okay this time. By the way, can I recommend you add your site address to profile signature?

You can get your own free WordPress blog mapped to own domain through WordPress:
http://en.support.wordpress.com/domain-mapping/

So you could just get started on WordPress service itself. I will always recommend you take time to buy a domain first and install WordPress into that instead. That way you don't have to bother exporting your WordPress blog data later on incase you are not happy with the domain mapping (not that I have tried it myself, but just by principle!)

first of all buy a domain and a hostin service, second download worpress from the wp site and that's all

WordPress can be built two different ways.The first and free one is to have them host it. I don't think you can change the domain name though.You could buy a domain and redirect it but I would just go with the second option.Domains given away with hosting can, but don't have to, be risky.You must be sure the domain is really registered to you and not the hosting company and that they won't make trouble if you want to move the domain to another host.

Nothing to do much for that, you just have to open wordpress.org site and do registration on it then you can see our own domain name blog and then you have to start to do insert your post thats it.

Wordpress.org is the best platform to create blog.

You can't get a free domain name. They're bought.

I knew about blogger and live journal but they do not let choose my own domain name. How to best host Wordpress on a with free domain? Any experience, feedback welcome

To create blog on wordpress you have to register first on wordpress as per your details which are needed on that. After that your account created and you can login to the wordpress. Now you can select the name your blog and put all the required information over there and share with people.You can  use the features for blog which is given in it.

I found something that may be of help to you, though the tips here might be just a bit after what you are asking about. Here you can read through a list of things to do after setting up a wordpress blog, so either way this would be a helpful link for you to go to. http://www.famousbloggers.net/43-blogger-tips-installing-wordpress.html