You can make a post in 2 ways.
You can go to the homepage and click in the what's on your mind box. This is kind of like when you put something on Facebook or Twitter. You can write up to 400 characters and also attach pictures etc.
If you are on your profile page click activity and again you'll see the what's on your mind box.
To make a blog post go to your profile and click Blogs. You will see any previous blog posts and a button that says New Blog, click it and it will open the blog editor window.
Just create your blog post and publish it. Your blog post will appear when it has been approved.
To create an article click on Submit an article in the User Menu.
This will open the article creation software. You can create your article and then submit it. Once submitted it will be reviewed before publication. This may mean a delay from when you complete and submit it to it going live.
For off the cuff posts it is better to use a blog.