You should forgive me for this. This long entry was supposed to posted last year but due to procrastination...
If you really don't want to muck around with renting virtual private servers so as to run a powerful microblogging script, you can cheaply and easily create a microblogging service using Buddypress . Buddypress is a Wordpress plugin which you can easily install to your Wordpress blog to create a microblog. Twitteronia (service unavailable) is one such instance using this plugin.

Installing Wordpress

The first thing we should do is to install Wordpress. Hope you've got your domain name and hosting ready at this point! Now:

1. Download all the files that are required: the latest Wordpress release, Buddypress zip files or tarball, and Buddypress theme files.
2. Decompress the Wordpress zip file or tarball and upload the folder to your server.
3. Login into cPanel (I'm assuming your host is using cPanel). Go to "MySQL Databases".
4. Now let us create a database.Go to "Create Database". Give a name to your database plus a secure password. Click "Create" to create your database.
5. Go to "Create User" and create a user for this database. Ensure that this database user has all the privileges of accessing the database.
6. Now let us edit this file: the "wp-config.php" file that is in the Wordpress folder you just uploaded. Mind you, you'll be using a text editor here (Notepad++is my favorite). You can also use cPanel's File Manager application that has a text editor to do this.
7. To edit the "wp-config.php" file, involves answering 3 secret questions and also inserting your database username, database name and password. Do just that and save your changes. (UPDATE: If you are using Notepad++ to edit this file, you'll have to edit the file on your computer first before uploading to your server).
8. Let us turn to installing your script. Point your browser to the installer script. This should bring up a form where you'll have to fill in the name of your blog, your admin name and admin password. Click on the "Create" button. The installer will now connect to the database that you created and create tables and then populated it with data.
9. You have now successfully created your Wordpress blog. Hurray! Celebrate. You can now start posting, changing its themes and toying around with its widgets but....

Hey! Weren't we out to create a microblog in the first place. Oops, there is still some work to be done.

For the creation of your Wordpress database, you can use PHPMyAdmin too. Simply go to PHPMyAdmin. This will bring up the homepage listing all the databases on your account. Go to "Create Database". Chooser a name for your Wordpress database and then create it. You don't need to touch the other selection lists on this page. Now your new Wordpress database will be added to the others on your account.

Installing Buddypress

You are just close to having your own microblog.

1. Upload the Buddypress zip files to the "plugins" folder in the Wordpress folder.
2. Go to your administration's panel. Under the "Plugins" section, your Buddypress plugin should be available. Click on "Activate". Wordpress will first unzip the file and then activate it. To bypass this, just unzip your Buddypress download on your computer and then upload it to the "plugins" folder. If you go to the "Plugins" section, Buddypress should be available. Activate it. This is quicker than the previous step.
3. Unzip your Buddypress themes locally and then upload them to the "themes" folder in the Wordpress folder. Now go to the "Appearance" section in your Wordpress administration panel. Activate the theme that you want.
4. Visit your blog. OMG, it just looks like a microblogging site.... with your blog's name on it. Now you can post status updates. To post entire blog posts you'll have to go back to your admin section and create an entry. Woo hoo!

The beautiful thing about this plugin is that has got cool themes related to it. If you just don't like the default theme or if you want to clone Facebook's theme, take a look at the Fishbook and FaceLook themes. Above all, you can use this plugin to create a microblog on shared hosting. Cheap, isn't it? For those who would love to bring in their friends into the site for some action...

Wordpress MU

...Wordpress MU is just the script for you. With this script, you can let in more users onto the site with only a single installation. Couple that with the Buddypress plugin and we'll be talking of an online microblogging service like these 10 sites..