Help…I’m creating a theme and now I’m stuck

I’m in the process of creating a theme from scratch, but would like to display my horizontal navigation bar like https://stereogum.com/

If you hover your mouse over there navigation bar(MP3 & Streams, Videos, Giveaways, etc), you see it drop down the reveal the latest post in that category. Can someone point me in the right direction, so I can figure out how to do something similar to that.

Any help is appreciated!