The default setting in WordPress is to allow commenting on Posts. This can be a real pain because spammer absolutely love to target WordPress comments. To change this default setting, go to here:
Settings -> Discussion
Turn off commenting on new articles.
Now all future articles will have commenting disabled.
To do this for legacy / older articles, you have to go into the article itself and them off one by one. If this is a heavy workflow then you will find numerous plugins to assist you with that.
Normally you also want to turn off
Allow trackbacks and pingbacks as this is also used for spamming.