Steps to Follow

0. Backup your sites

Generate a full site backup in cPanel. It might also help to copy all the files on the server via FTP, so that you can easily access the files for plugins and themes, which you'll need in a later step.

1. Export from your existing WordPress installations

In each of your existing WordPress installations, go Tools > Export in WordPress. Download the WXR files that contain all your posts and pages for each site. See the instructions on the Tools Export SubPanel.

Make sure that your export file actually has all the posts and pages. You can verify this by looking at the last entry of the exported file using a text editor. The last entry should be the most recent post.

Some plugins can conflict with the export process, generating an empty file, or a partially complete file. To be on the safe side, you should probably disable all plugins before doing the exports.

It's also a good idea to first delete all quarantined spam comments as these will also be exported, making the file unnecessarily large.

Note: widget configuration and blog/plugin settings are NOT exported in this method. If you are migrating within a single hosting account, make note of those settings at this stage, because when you delete the old domain, they will disappear.

2. Install WordPress 3.3.1

Install WordPress 3.3.1 to the root of your public_html directory. It has to be at the root or the multi-site feature won't work. Follow the instructions for Installing WordPress in the Codex.

3. Create a wildcard subdomain

Create a wildcard subdomain. This should be as easy as going into your web hosting control panel and creating a subdomain named *. If you're not sure, ask your host for help.

4. Activate multi-site

Activate multi-site in your WordPress 3.3.1 install. This involves editing wp-config.php a couple of times. You need to use the subdomain, not the subdirectory, option. See the instructions in the codex on how to Create A Network.

5. Create a test blog

Create a test blog in the WordPress Network Admin > Sites panel. It should show up as subdomain.yourdomain.com. Test the blog to make sure everything is working correctly at this point.

6. Install the WordPress MU Domain Mapping plugin

Install the WordPress MU Domain Mapping plugin. Folllow the installation and configuration instructions in the readme.

7. Create blogs for each site you want to import

Create blogs for each of the sites you want to host at separate domains. For example, importedblogdotorg.mydomain.com.

Note: choose the name carefully, because changing it causes admin redirection issues. This is particularly important if you are migrating a site within the same hosting account.

8. Import WXR files for each blog

Go to the backend of each blog, and import the exported WXR file for each blog. Map the authors to the proper users, or create new ones. Be sure to check the box that will pull in photos and other attachments. See the instructions on Tools Import SubPanel.

Note: if you choose to import images from the source site into the target site, make sure they have been uploaded into the right place and are displayed correctly in the respective post or page.

9. Copy theme and plugin files

Before you start, check that your plugins will work in the network installation. If a plugin is not supported, do not install it. Find suitable alternatives for it by searching for the plugin's function with "multisite" or even "mu", as in "social bookmarking plugin wordpress multisite".

Copy the theme and plugin files from your old WP installs to their respective directories in the new wp-content. You can activate themes for the network, or you can go to Superadmin > Sites, then click edit on the site you want, and enable a given theme for just that site.

Note: if you are using a child theme, copy both parent and child themes to the new site.

10. Edit WordPress configuration settings for each site.

Edit the configuration settings, widget, etc. for each site. By the end of this step, each site should look exactly as it did before, only with the URL subdomain.yourdomain.com rather than its correct, final URL.

11. Connect domains to your main site

For each of your domain names, point them to your main site using Apache Virtual Hosts. You can usually do this easily in cPanel.

Sometimes (not always) this is referred to as "parking". If you've been using the domains as add-on domains, then you need to delete the add-on domains first, then create the parked domains.

The domains that you wish to park must be pointed to the nameservers of your hosting provider, or they must have DNS entries pointing them to the same IP addresses.

12. Map the domains

In Superadmin > Sites, find the new site's ID.

Then, go to Superadmin > Domains, and map the new site ID to the publicly-visible domain name.

To redirect example.com to www.example.com, create two mappings, making www.example.com the "Primary" mapping.

NOTE: You only need to do this step if each site you are importing had its own domain name. If they were subfolders or subdomains originally, you can skip this part.

Potential Problems

Limitations of PHP configuration

You may run into trouble with the PHP configuration on your host. There are two potential problems. One is that PHP's max_upload_size will be too small for the WXR file. The other problem is that the PHP memory limit might be too small for importing all the posts.

There are a couple ways to solve it. One is to ask your hosting provider to up the limits, even temporarily. The other is to put a php.ini file in your /wp-admin/ and /wp-includes directories that ups the limits for you (php.ini files are not recursive, so it has to be in those directories). Something like a 10 MB upload limit and a 128 MB memory limit should work, but check with your hosting provider first so that you don't violate the terms of your agreement.

Search the WordPress support forums for help with PHP configuration problems.

Converting add-on domains to parked domains

Deleting add-on domains in cPanel and replacing them with parked domains will also delete any domain forwarders and e-mail forwarders associated with those domains. Be aware of this, so that you can restore those forwarders once you've made the switch.

Limitations of importing users

As there is the above way to import the content into an instance of the Multisite-blog, you are running into massive troubles, when it gets to import multiple users. Users are generated during the import, but you won't get any roles or additional information into the new blog.

Losing settings

If the old site is no longer available and you find you have forgotten to copy some setting or you want to make sure you have configured everything correctly, run a google search for your site and then click to view the cached version. This option is available only until your new site has been crawled, so you'd better be quick.

Losing embedded content

When you are importing a single blog into a WordPress Network ( Multi-site ) then your embed html and such will be stripped currently. The solution is to use the plugin Unfiltered MU. Preferably use the mu-plugins folder for that plugin. After you have activated / installed the Unfiltered MU plugin your import will now leave the imported content as is.