I"m happy to hear you are using version control. In addition to letting multiple people work on the code base, it provides history. Which saves your bacon if there is a problem!
Jenkins is a
Continuous Integration server. What you do is set up a
job on Jenkins to automatically
build the code every time someone pushes to the repository. Building consists of compiling, running any tests you have and optional other steps. There are two ways to configure this. You can use
polling where Jenkins asks git periodically if there has been a push. Or you can use a git
hook to have github inform Jenkins about the change.
The words I underlined in the previous paragraph are concepts and apply to other tools; not just Jenkins.
Consider using
Travis CI instead of Jenkins. Travis is free for open source projects. Many FIRST teams share their code and you even said yours is public; so you'd qualify to use it for free. The advantage of Travis over Jenkins is that you don't have to install a CI (Continuous Integration) tool nor do you have to maintain a server or pay for cloud hosting. Travis also integrates with github out of the box. It's not hard to configure Jenkins to do that regardless.