How to store data having a fixed number of columns and a variable number of rows
Based on your image, something like the following will be fine (using a RDBMS solution):

create table articles
(
  article_id     integer PRIMARY KEY,
  title          varchar(256) NOT NULL,
  url            varchar(256) NOT NULL,
  summary        varchar(256) NOT NULL,
  body           varchar(4000) NOT NULL
);

create table article_comments
(
  comment_id    integer PRIMARY KEY, -- primary key, unique, does not map to the "comment number" in your question
  article_id    integer NOT NULL, -- references articles.article_id
  screen_name   varchar(100),
  disqus_url    varchar(256),
  comment_dt    datetime, -- both the date &amp; time from your spreadsheet
  comment_text  varchar(4000),
  comment_url   varchar(256),
  comment_post_id varchar(25)
);


Basically, there's a one-to-many relationship between articles and comments.

You don't say what RDBMS you'd want to use, so the data types will need changing accordingly (bigger VARCHARs/TEXT columns etc will be needed for long articles/comments etc). Constraint DDL is also largely RDBMS-dependent, so you'll have to look the syntax up for yourself once you've made a decision. I can recommend Postgres.