A tutorial on how to submit a solution to Kattis is found here: https://bridgewater.kattis.com/help/submit.
One way to submit a solution is via the Kattis website. To do so, navigate to the problem description webpage for the problem you are working on. On that page you will see a submit button in the upper right corner.
When you click on Submit you be directed to a Submit Solution page like the one below.
Here you select the files you wish to upload and specify the name of the class that has your main() function. After you drag and drop your files and enter your Main class you Submit Solution page should look like the image below. When done, press Submit.
When you press submit you’ll get a screen that looks like the following.
The “? New” status means that your solution is currently being judged. In about a minute, you should receive an email from the system with a judgment like the following one.