Cut to other page from main article

I have a second WordPress site I have made for my husband’s and my business. It is based around reviews, so there are articles in it. I want to do cuts, where you only see part of the article on the main page and then open to the whole article on another page. But I’m a WordPress idiot.
Any advice?

This is what I have: http://www.1013musicreviews.com/
This is what I am looking for: http://musictourreviews.com/

See how the second one has only one photo and some wording on the front page, only to open to a full article with more images on another page? That’s what I’m looking for. I have seen that called cutting on certain websites, but I don’t know what it is called on WordPress. I’m sure it’s something easy, as a lot of people do it, but I am just missing something. Please explain this thoroughly because I don’t know what I’m doing.

Thank you!