Find some good Sites of Directory Submission in Google, Then select Category & sub-category if available, Click on submit option or add site option it differs sites wise. Now see whether you have to go for pricing for Free submission & fill the fields. Here is the easiest way to Submit Directory submission
Dmoz : No need to submit again. wait. your site will be approved. if you resubmit the chances of listing can go down.
Well when you get some directory list then "submit a link" then select the free submission and then fill the form which have different cells. Fill it accordingly and select the relevant Category & sub-category and description of your site. Check it's indexing in Google first.
how to submit, well thats what you can see its easy try to read the site you will get options to submite your site and more like that.
As what you've stated, your blog is a newspaper type. In submitting your blog in directory you need to choose the proper category. Since your blog is about news then put it under News and Media (if there's a category) or just choose the very appropriate category which you think fits your blog. Hope this helps you.