Well, if you want new, random readers then I'm sorry, you can't block them from your blog. If new people aren't a concern to you then yes, you can keep someone off your blog. This is what you do:
1. Go to your Blogger dashboard
2. Go to Settings for the blog you want to make private
3. Go to Permissions
4. Where it says Blog Readers - Who Can View This Blog?, choose the option that says Only People I Choose
5. A box will open up that says invite some people to read your blog. Enter the email addresses of the people you'd like to invite separated by commas. You can invite up to 100 people.
Now your blog is private and only people that were invited to read it can view it. If someone that has not been invited goes to your blog URL they will get a statement saying "We're sorry, it doesn't look like you have permission to view this blog".
Now, if you're like me and love visitors even if you have no idea who they are, that option will not work. You can, however, block someone by IP address. First you'll need their IP address for this to work.
It's really easy to get someone's IP address if you are using Site Meter. Click here to learn more about Site Meter. It's partway down the page after my prizes..
Once you have their IP address, go here
Follow the instructions they give and then that person will be blocked.
Another interesting deal about blocking people by IP address is that my new comment form has that built right in. When someone leaves a comment, I have the ability as administrator to block their IP address directly from their comment. It's just another plus I think :) You can click here to learn more about the IntenseDebate comment form.
I would suggest a few of things before you go through all of the above though.
1. If the offending person is someone who comments often and you are just irritated by them, just talk to them directly. More than likely you can resolve the problem by being open and honest if both people act reasonably. Don't be hateful about it. There's no reason to hurt anyone's feelings but tell them, hey, this is bothering me...If they still don't want to cooperate then block them.
2. Post a Blogger's Disclaimer on your blog and write a post explaining it. You can post the Read Me disclaimer or write your own or do both like I did for my Happy At Home blog. If people don't respect them, block them.
3. If the person is someone you know personally, again, talk to them. Tell them that their comments are hurtful for you and that your blog is your place to express yourself and that you would appreciate either respectful comments or no comments at all. This is covered under the Read Me disclaimer in #2.
4. If the person is an out and out spammer like the oriental "each dot = a porn site" spammer that is making their way around Blogger, report them using the report button at the top of their site or by copying their profile address or comment with username and going to Blogger help. Then block them.