The reason you probably don't see any job openings because you haven't been added to a hiring team yet. Every job opening has its own hiring team.
The colleague who added you to Homerun, can also add you to the hiring team of the jobs you need to be involved in.
If you do not see any active jobs, reach out to your colleague to help you with this. They can invite you to a job opening by following this article.
Once you have been invited, you will see these jobs appear under 'Your jobs' at the left-hand sidebar.
You can also find these jobs via the 'Jobs' page. Click one of the jobs and explore the Job post, Candidates and Apply form via the menu bar at the top.