Syndicating your RSS feed (see more here: Syndicating your RSS feed with Technorati): Syndicating your feed helps promote visibility of your site. Anybody who goes to technorati to search for blogs on a specific subject will have a better chance of finding your site if you proactively connect with technorati.
Using technorati to provide search (see more here: the Technorati Searchlet): Technorati is part search engine, and you can use that search engine from your site. On the page linked here you get instructions on adding a bit of code to your site that allows users to search your site. On requesting a search they go to Technorati's site for the search results, and the search results should come from your site only.
Your Technorati profile: Technorati allows a blogger to sign up and get a user id with their service. Once you're registered with technorati you can "claim" multiple blogs, and in general you'll have a "profile" page published by technorati that gives the public a short rundown on who you are.
The first step is to sign up with technorati. Simply go to their home page and click on the "sign up" link. They ask for a few things like your name and email address. Once signed up you can claim one or more blogs as being yours. The process is relatively simple but has room for confusion.
Once signed you click on the "blogs" link and it shows the list of blogs you've claimed. At the top of the page is a text entry box where you give the URL for a blog you want to claim. Enter the URL for the blogs main page. On the next page you're given a bit of javascript code. Unfortunately they simply say to paste this into the template for your home page, but they don't tell you what that means. Unfortunately each of the blog software packages does this differently and it would be very difficult for them to give instructions for every blog package. Fortunately it's not hard, and unfortunately it varies so much from blog package to blog package that I'm not able to give better instructions.
So, paste the code they provide into the template for your site.
Once you have the code embedded you can configure the blog claim. This means giving a description of your blog, some keywords describing the blog, and a configuration of what the javascript code actually does. This javascript will cause several things to appear on your web page, and you can control what they are. Currently the choices are to embed a technorati search box, embed a link to your technorati profile, and embed a link to show what blogs link to your site.