If your car is pretty old and you live in the salt belt region, or your car generally is very rusty this may not be the best job to do on your own unless you have proper tools and experience working on cars. Rust slowed me down heavily. Even with a ton of PB Blaster, 22 inch breaker bar, and an impact gun, I had some difficulty getting pieces apart. We had to resort to using a torch at one point.
Tools I used (may not be all inclusive):
Ratcheting Wrench w/sockets and box ended wrenches in 12mm, 17mm, 19mm, 22mm
Lift or Jack with jack stands
If I have the terminology correct, what I actually broke was a control arm. The lateral link is the secondary pieces closer toward the front of the vehicle.
First thing is to disconnect the end links from the control arms. I don't have photos of this because I ended up removing the entire sway bar as part of another upgrade. It's pretty straight forward. I had problems with rust here, but all you have to do is unbolt the nut and bolt from the bottom portion of the end link that goes thru the bracket on the control arm.
I have aftermarket endlinks so yours may look different. Also ignore the socket. I was just sizing for a future step.
You can start to see the amount of rust and deformation I had on the bolt. I ended up having to use a hammer and a punch with a lot of PB Blaster to get it out. Destroyed the bolt. Luckily I'm replacing the whole setup.
After they're disconnected, you can just twist them out of the way.