How can I find questions that I can contribute to on Stack Overflow?

Use filters to narrow down questions which you can answer. Go to Stack Overflow and click on 'Unanswered', and then 'Newest'. Newly asked questions will show on top. Then you can select 'Tags' on the right side of the page, to further narrow down. You can search based on several different criteria.

Go through questions one by one, and answer if you know the solution.

As Jayesh Chandrapal mentioned you should narrow down the search. The initial feed you see is not necessarily the newest question. So go to the newest question tab and you can see a vast number of unanswered questions.

In other note you can search for a tag you exepertised and then go to the newest question tab.