What did you do, pick the very first picture when you googled swing dancing? (Yeah, I know you did) With country music, it is usually known as the swing, in others, it goes by the jive. Either way, you are a lloonngg way away from what you see above. You and your partner have to really trust each other or someone's getting seriously hurt. At first, it will look like the one in the middle.
Then eventually, you will get to the one on the bottom.
The people who do the one on the top have spent years and years perfecting it. So get your fanny down to a honky-tonk night club and get started little lady.
When I lived in Albuquerque, they took a giant store, gutted it out, and made one huge dance floor in the middle with seating all around it. Do the still have Gilley's in Texas? Many of those types of places have routine dance lessons. You don't need a partner, just get out on the dance floor, and they will start you off with the basic steps. After a while, you will be the belle of the ball.