Want to start a simple machines forum for a class

[churnbabychurn]

My understanding is that I just need to download the free forum software onto my computer and then set it up. Is it really that simple?
Also can a small forum run on my own PC?

[whYME]

Is it really that simple?

No.

Also can a small forum run on my own PC?

Technically speaking, yes.
(As long as your ISP isn't blocking port 80 or it's running on a local network.)
To do that you'll need to install a web server (software) on your PC.
Unless it's only running on a local network you probably don't want to do this. Buy hosting.

My understanding is that I just need to download the free forum software onto my computer and then set it up.

No, you download it to your PC then upload it to your server & run the installation.
Some hosting providers might have an option of installing it directly from the Control Panel.

[churnbabychurn]

Oh.
thanks 

[MarkS]

Look into Moodle with a freewebclass site.

https://moodle.org/
http://freewebclass.com/

You can set up a group with a primitive forum but a better overall structure for uploading learning materials, making a calendar of classes/exams, etc.