It looks like currently you have your OpenCart website in maintenance mode, so we can't see what issues might be happening with your checkout at the moment. Did you get any errors when attempting to click the checkout button? Did the site appear to be loading or doing anything at all while you clicked the button?
You can take a look at our guide on managing shippers within OpenCart which details setting different shipping methods to active. One of those being the Flat Rate method.
Please let us know if you had any further questions.
I didn`t get any errors. At first it asks to apply shipping and when I apply it doesn`t ckeck out. Just click a checkout button and nothing happens.