One of the greatest gifts I think you can give your blog is a burned feed from
Feedburner. Here's the scoop, in the usual what / why / how format.

What is it?: A feed is a version of the material that you post on your blog that is publishable on other sites and readable in "feedreaders" like bloglines and kinja. These services let you keep current with multiple blogs at once.
Feedburner explains it all:

Consumers use RSS reader applications (or one of a growing number of online services) to collect and monitor their favorite feeds in one place (RSS content from a publisher, viewed in one of these readers, is often called a "feed"). RSS makes reviewing a large number of sites in a very short time possible. RSS [also] permits instant distribution of content updates to consumers.

There are 2 main kinds of feed - atom and RSS. Blogger automatically generates an atom feed for your blog.

Why change it?: A lot of feedreaders don't read atom, & although it is possible to have a second feed in RSS format, that's confusing for your readers & possible subscribers, & feedreaders that index the way a search engine would won't see the second feed anyway.

Blogger only offers an atom feed. Feedburner feeds are "smart" & can take an atom feed & turn it into RSS, meaning that you can offer one feed that can be read in multiple formats.

Feedburner "smartcast" will automatically add rss headers to any sound file that
you link to, turning it into a podcast.

The feedburner "chicklet" displays the number of subscribers that you have right
on your blog, giving possible subscribers some sense of how hot your content is, & helping them to join in!!

The feedburner feed is browser-friendly & doesn't look like code, so the nervous
subscriber is soothed & reassured as they sign up for your content.

Update: As Fritz points out in the comments, & I neglected to mention, the other reason to switch is for Feedburner's stats, which will let you see how your feed was accessed, how many people subscribe, and what the recent trends are, as well as which posts from your feed are attracting attention. Sign in to feedburner once you're all set up, & select "view stats"....

For other services & options, see the Feedburner's info for publishers.

How do I do it?: Ah, the tricky part.... It isn't impossible, but it's slightly involved. There are two main parts

Step 1: Sign up for the feedburner feed by following their "blogger quick start" instructions in the top right of the main page.

Enter the URL of your blog on the Feedburner main page, & click next.

Select the services you'd like with your feed.

Confirm the services & activate the feed.

Place a link to the feed on your blog.

Step 2: Edit your template so that readers will see your new feed and not the default atom feed. This is recommended but optional. Read it through all the way first!!

View the source for your web-page in a text editor (view -> page source or similar)

Copy out the Meta-tags. If you haven't messed with these before, they begin with <meta and end with a closing style tag </style>. Blogger inserts them all
with one tag, so you won't see them in your template, which is why you have to view source. Mine look like this:

<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
<meta name="MSSmartTagsPreventParsing" content="true" />
<meta name="generator" content="Blogger" />
<link rel="alternate" type="application/atom+xml" title="blogname" href="http://blogURL.com/atom.xml" />
<link rel="service.post" type="application/atom+xml" title="blogname" href="https://www.blogger.com/atom/*********" />
<link rel="EditURI" type="application/rsd+xml" title="RSD" href="http://www.blogger.com/rsd.g?blogID=*********" />
<style type="text/css">
@import url("http://www.blogger.com/css/blog_controls.css");
@import url("http://www.blogger.com/dyn-css/authorization.css?blogID=*********");
</style>

Paste the meta tags that you copied from the text editor into the head of your
blog template, immediately before the existing blogmetadata tag. (no good reason
... just easy to remember....)

Delete or hide the blogmetadata tag. You just replaced the single automatic blogger tag with the complete text of each individual meta tag, so you don't need it any more.

Now, after all that, there's one and only one line that we're going to edit. Be careful not to edit neighboring lines because they control the "e-mail this post" and "edit this post if I'm logged in" icons, & we don't want to break those.

The only line we're messing with is the autodiscovery tag. It looks like this: <link rel="alternate" type="application/atom+xml" title="blogname" href="http://blogURL.com/atom.xml" />

It currently points to the atom feed from blogger and we want it to point to your new feed. Simply change the URL at the end of the code from the blogger / atom URL to the URL of your new feedburner feed. And we're done. Now if any feedreaders come a-crawling they'll detect your new feed and not the old one. For more info, & to see the poor folks at Feedburner answer the same question eighty-three times over for everyone who ever tried this (including me...) check out the feedburner forums tech tips "track all your traffic" thread!!

For bloglines - If you have an established site & bloglines already tracks one or more of your feeds, they won't stop using the old one automatically. If you e-mail them, however, they'll find the new feed & offer it to your readers. They are fine and helpful people!!

Have fun with feedburner!! Please add to this how-to in the comments if there's clarification required.

See other posts in Blogger Hacks: The Series