Quick Start Guide:

First of all you need to create an account. For this, click the Account button in the navbar. When you want to do an action that needs an account you will be requiered to log in. For example see last step in the Submitting part.
In order to take part in a contest you don't need to register to a particular one. You just need to access its page after the contest starts.
To submit a solution you can either paste your code into the text area for the corresponding problem or browse for the source. In what follows you can see all the steps for submitting:

STEP 1: Choosing a problem from the list

In order to choose a problem click the Problems button from the navbar.

Then click on the problem you want to solve.
For example let's choose A+B problem.

STEP 2: Starting to fill the form

From now on we focus on Submit solution area.

Here we can find the form to be filled in order to upload a solution to any given problem.

STEP 3: Solution source code

1st Option - Upload the source file

Go to Choose file button from File area and then choose the source file.

or

2nd Option - Paste the code

Here are some examples for how to submit:

STEP 4: Selecting the file format

After uploading the source code we have to choose the format corresponding to the code we provided as solution.

...and SUBMIT

Click the Submit job button and wait for the results.

You will be redirected to Job log page where you can see the results.

Good luck!