This is a re-post, since I've already posted these instructions and emailed them to various people many times. But I thought I'd reiterate the thought, since I continue to be frustrated when I can't reply to certain comments, and because I've added helpful images of what you should see at each step.
If you're not sure if this applies to you, go through the steps anyway and check that everything is in order.
Don't just do it for me, do it for yourself!
How To "Show" Your Email Address and Have Replies to Comments You Leave Emailed To You:
Go to the blogger dashboard. On the left, next to your photo, there's a list of links:
Click edit profile.
Then below, under the "Identity" section, it shows your user name (your personal email address you used to sign into blogger and create your blog) and right below that there's an email address box. If it's the same as your personal email address, and that's not the email address you want to use to receive/reply to/and get replies to your comments, change it to your blog's email address.
It wont have any effect on your management of the blog, and it wont change the email address you use to sign into blogger, but it will be the email address that other people reply to when you leave comments. But make sure you've checked off the "show my email address" box above in the "Privacy" section! Then click save profile at the bottom of the page. And you should be all set!
How To Get Your Comments E-Mailed To You:
Go to the Blogger Dashboard, then to Settings,
and then click on the Comments subtab.
Scroll down to the bottom of the page to the Comment Notification Email box.
Put your email address in that box, and instead of checking your comments directly on your blog, you'll get an email for every comment you receive. Then to reply to the comment, you just reply to the email from your inbox. If you don't want people to see your personal e-mail address, do not use your personal e-mail address to receive your comments, because when you reply to them, it's the address people will see. If you don't already have one, you might want to make an e-mail address just for your blog (for example, mine is: firstname.lastname@example.org) and put that one in the Comment Notification Email box. You have to remember to check it though!