How to allow users to comment on blogs

If you want anyone to comment, then go to Settings > Discussion and check “Allow people to post comments on new articles”.
Then consider carefully the rest of the options on the Discussion area.
Any previous posts may have this disbled, so check each post or allow comments bulk in the Posts list.

This is not quite what I want. I want people to be able to comment, but register first, without having to send a request that needs approval.

I am new to blogging, is this a common requirement, how is this normally set up?

Steve

Then, you would have them become Subscribers and decide if you want to approve new registrants or let anyone register. Subscribers can only read posts/pages.

To have people register without your approval, set these options:

Settings > General
Membership > Anyone can register
New User Default Role > Subscriber
(For reference, here are the WordPress Codex : Roles and Capabilities)

Settings > Discussion
Default article settings
> Allow people to post comments on new articles
(just what it says)

Other comment settings
> Users must be registered and logged in to comment
(just what it says)

Email me whenever (these are optional)
> Anyone posts a comment
> A comment is held for moderation

Before a comment appears (these are optional if you want to approve comments before they show)
> Comment must be manually approved
> Comment author must have a previously approved comment (optional if you have approved a previous comment of a person)

If you want to approve people before they can be Subscribers on your site, then you need a Registration plugin such as: New User Approve or User Registration Aide

I wrote a custom-plugin with a short-code that goes on each page where allow-comments needs to be overridden to allow it, because I was frustrated with the general settings not working; but it is not yet prime-time for general release.

@stephen

Nice but, how does the plugin auth new users? To allow to comment?

Without that particular plugin, one option might be to create a separate database outside of WordPress (say a different database using MySQL). That database would have users and comments as well as administrators and authorizations setup in tables. You could create a registration page that would update your database the way you would want it. Then you could use MySQL queries (and maybe there are existing WordPress plugins for that although CGI scripts are my current preference) so you could have your php code that would run to complete what you are asking for. I use the insert-php plugin to write php code directly within the page to prototype with.