To install Mathematica on your computer,

1) First, you need to request a Mathematica activation code by sending an email to  softwarelicenses@science.oregonstate.edu with the subject line "Mathematica Code Request". You can just say that you need it for Math 252H.

2) The university will send you a code of the form ****-****-****** 

3) Go to https://www.wolfram.com/mathematica/trial/ to download a trial version of Mathematica 11.3.0. You will need to sign in with your Wolfram account which you created earlier. If you haven't created a Wolfram account, make sure your create it using your OSU's email address.

4) Then install Mathematica on your computer. At the same time, your will get an email from Wolfram with the subject line "Your Mathematica trial has started" with an activation code for your trial version (different from, but of the same format as the code OSU provides in Step 2). After the installation finishes, enter this code, which will activate your trial version.

5) Close Mathematica, and open it again. On the top right of the application window, you will see a line "Enter activation code" next to "Buy". Click on that, and enter the code OSU provides. Close Mathematica, and open it again. The message "Trial version" should disappear.
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Sydney Andersen shared with me an alternative way to install Mathematica as follows (Thanks Sydney!) I quote her message:

"Mathematica can be accessed without download, and from any computer, using OSU's Citrix receiver. The process is outlined below:
- Search apps.oregonstate.edu in your web browser
- Login using your ONID username and password
- Go to the 'Apps' tab
- Find and select the desired program (in this case, Mathematica)
- Allow the program to load, which may take a few seconds
- In tiny letters somewhere, there should be the option to use the lite version if you do not wish to download Citrix to the computer."