If you want to use blogger using your own domain name all you have to do is follow these instructions -> http://help.blogger.com/bin/answer.py?hl=en&answer=55373

If you want to use Moveable Type or Wordpress you will need to also have your own web server. With your own web server it's just a matter of uploading some files and running an install script. The instructions for Moveable Type are here -> http://www.movabletype.org/documentation/installation/ and Wordpress installation instructions are here -> http://codex.wordpress.org/Installing_WordPress

I use Wordpress because it has a great community and is a mature blogging platform. Plus with all the extensions out there you can customize your blog to fit your needs. I host it with Dreamhost which is a fairly cheap but very robust. Dreamhost has a one-click install process for setting up a new Wordpress blog. This makes it a snap to start a new blog as well as updating
the core files. Unfortunately, Dreamhost doesn't have a one click install option for Moveable Type but you could always install that manually.

More info about Dreamhost can be found here -> http://www.dreamhost.com/r.cgi?174422

Forget Blogger -- it is too simple and restrictive. You will end up regretting your decision and want to switch to a fully-featured blogging system later, which is more of a hassle.

You can use Moveable Type, though Wordpress is a lot more actively developed these days. Look at the features of both and see which you think suits your purpose most. Also look at the templates available for each to see which you'd like.

Now, as for hosting, you should make sure you get LINUX hosting, not Windows. This doesn't mean that you need to know anything about Linux yourself, don't worry, but a lot of the blogging software requires Linux software to be running on the host. Your host also needs to give you MYSQL databases... make sure they are not too restrictive on this.

As for setup, the manual method takes some editing of configuration files, but if you have a host that supports ONE-CLICK INSTALL, you won't have to bother with any of that. You'll just click 'install' and then be able to login to your blog and set up the multiple authors and everything else you want.

I use AN Hosting, which has the one-click install, and allows you to host unlimited MYSQL databases. It costs $6.95 a month -- that allows you to host multiple sites and includes the domain name cost.

I've also used 1&1, but they don't support the one-click install, and you need to follow some technical setup with them.

WordPress is currently the gold standard of blogging... I use it!
http://en.blog.wordpress.com/2006/10/24/domain-mapping-registration/

Typepad also offers this service:
http://www.typepad.com/

The Quick Answer with Blogger:

Buy your own domain, and create a CNAME record for it to point to ghs.google.com (unless you buy the domain through Blogger).
Enter your domain in the 'Custom Domain' option on the Settings | Publishing tab.

Longer answer:

Publishing on Blog*Spot is the fastest and easiest way to use all of Blogger's great features. (And for free, no less!) If you don't care to have blogspot.com in your blog's address, though, you can get a domain of your own. We'll continue to host all your content as before, but it will be displayed at your new address. (Unlike FTP publishing, which requires you to buy both a domain name and a hosting service.)

Choose and Register Your Domain

The first thing you'll need to do is to choose a domain name, like mysite.com and register it. You can register domain names from any of a number of different registrars, and you can use .com, .org, .net or any other valid addresses. Remember: you only need to get the domain name; you don't have to pay extra for hosting service. The easiest way to register a domain is to buy your domain directly through Blogger. If you go this route, we'll automatically configure all of your relevant DNS settings and attach your new domain to your existing blog immediately.

Update the DNS Settings

DNS stands for Domain Name System, and a DNS server determines what site a given address takes you to. So far, you have a domain name but none of the servers on the internet know what to do with it yet. To take care of this, you need to create a CNAME record for your domain with the DNS, associating your domain with ghs.google.com. The exact procedure for doing this varies depending on your domain registrar, but you can find instructions for many common registrars here. If yours isn't listed, or if you run into other difficulties, you can contact your registrar directly and they'll be able to help you out.

Once you've told one particular DNS server about your new domain, it will have to transfer that information to all the other servers on the internet, which could take a couple of days. So be aware that your new domain won't necessarily be working instantly.

Update Your Blogger Settings

Almost done! At this point, you have a domain name, and the DNS servers know to direct people to Google when they want to see your blog. But Google hosts lots of blogs, so we have to make sure the right one is associated with this domain. You'll do this on the Settings | Publishing tab for your blog in Blogger.

I would like to start by saying that WORDPRESS is the best way to setup a blog but since you wanted to know about BLOGGER or TYPEPAD so i would advice you to go with BLOGGER, its the 2nd best.

http://walhez.com/wp-content/uploads/2007/10/blogger_logo.png

Here's how to set up your Blogger custom domain:

Decide on your domain name, and register it with a domain name provider. There are literally hundreds of sites you can use (just do a Google search for "domain name providers"). My provider of choice is GoDaddy.com, since this site offers very low cost domains with free hosting, free email accounts and other features too. I'll explain shortly why having free hosting is very beneficial.

Once you've registered your new domain name, you'll need to change the DNS settings. DNS stands for Domain Name System: a DNS server determines what site a given address takes you to. You need to tell the DNS servers that visitors to your custom domain should be directed to your Blogspot blog, which is what we're doing here. You need to access the control panel for the DNS settings associated with your domain. Take a look at the CNAME records here. Is there a name/sub domain called WWW? If there is, you'll need to edit this; if not, you'll need to add a new CNAME record. In either case, you should enter the correct information as I'll explain next.

For the name/sub domain (this depends on what your provider calls it!), enter "www" and save (or click continue).

For your target host/destination/record (again, this is provider dependent) you need to enter "ghs.google.com". Save and continue. This is all you need to do with your domain provider!

It may take a few days for the DNS settings to come into effect, so it might be worth waiting a day or two before completing the next step, which is to associate your Blogspot account with your new domain.

Now, you should log into your Blogger account. In the "settings" area, click on the "publishing" tab near the top of the page and choose to set up your custom domain. In the text box, enter your new domain name (eg: www.example.com). Now when you preview your blog, you should see your custom domain in the address bar instead of your blogspot one!
Your old Blogspot address will automatically forward to your new domain, so you don't have to worry about losing any traffic. Also, since Blogger still hosts your domain, you'll have no worries about hosting or bandwidth.

However, there are a few points you should take note of when publishing to your custom domain.

Most important is this: you can only post to http://yourdomain.com or http://www,yourdomain.com. NOT BOTH! So before you enter your domain name in the Blogger settings be sure which of these you prefer to use.

My advice would be this: try to use a domain provider which offers some free hosting with your domain (this is why I'd recommend GoDaddy) and set your blog to be hosted at www.yourdomain.com. Then upload a simple redirect page as your index to your hosting account, which will redirect any visitors to www.yourdomain.com instead.

http://www.onlineopportunitiesreviewed.com/wp/images/godaddy.gif

I don't consider this to be much of a problem. In fact it can be an advantage: having only the http:// or http://www in your blog address is that your Technorati ranking will be improved, since there will not be two entries for your blog (one at each sub domain, a problem I used to have with a hosted Wordpress blog). By redirecting your readers, they will always know where to find you, and you won't lose any traffic.

Four basic choices:

1. Free provider that allows you to point a domain to it (Blogger, Tumblr, etc.)
Google is a little picky about the external domains, it wants you to use CNAME records instead of A records, which I prefer. Tumblr simply asks you to setup an A record. My main blog at http://insomniaccoder.com is a Tumblr blog with an A record for my domain.

2. Free provider that charges you to point the domain to it (Wordpress.com, etc.)
This could have changed since I checked, but pointing your domain to a Wordpress.com blog was considered an extra so you had to pay to unlock the feature. Note that I refer to the wordpress.com hosting service, not to Wordpress blogs that you host on your own.

3. Any provider, and you setup a redirect from yourcustomdomain.com to yourblog.yourblogprovider.com

If you have control of your DNS, you probably have a URL redirection feature. This lets you use your custom domain, but your users get bounced immediately to the blog provider's address.

4. You get a hosting account and set the whole thing by yourself.
This is the most effort, but also more control to you. If your hosting account doesn't allow you to do this, you are getting ripped off. I run my own hosting company and even my cheapest plans (I host Wordpress blogs starting at $10 per year) have full control of their DNS.

Since your preference is blogger, then you'll have to deal with the CNAME hassle. From experience this works perfectly if you use a clean domain name that you are not using anywhere else. If you are running some of it in Google services and some elsewhere, then it is downright annoying.

Blogger can do this right out of the box. Just set up the blog on Blogger, and then go to the blog settings menu, under the Publishing tab, and then you can buy the domain name directly from eNom or GoDaddy from right there and set it up.

Go to a web host like Site 5, purchase the domain you want, and then easily install the blog. I suggest you use Wordpress. You can easily set up different user accounts so that the 3 or 4 people writing the blog have their own unique logins. You are going to have to pay a small amount per month (less than $10).