Live corners are a fast and easy way to manipulate corner points in Illustrator to change their shape. You can easily create complex shapes from simple paths using live corners, so let me show you some quick examples and then you can get started working on your own projects.
First I'm going to show you how Live Corners work on a square.
When you first switch to the direct selection tool, all the corners are usually selected. You can manipulate them all together by clicking and dragging the live corner widget until you're satisfied with the corner radius.
If you want to manipulate one point, just click the corner you want, release, then click and drag it. Note that the selected corner widget looks different from the unselected ones.
You can select multiple corners at once by holding down the shift key while you click each one.
As you can see, manipulating multiple points at once can give you different effects. One thing to keep in mind is that pulling multiple points at once can reduce the maximum achievable corner radius. So if I'm manipulating one point I can pull it all the way to adjacent anchor points before it turns red. If I'm pulling multiple corners, I can only go as far as the new anchor points that the tool is creating.
You can also change the type of corners you use. One option is to double click the selected points you want to change and select the type you want from the dialog box. Our options include a rounded corner, which is the default, inverted, and chamfer.
Alternatively, you can hold the alt or option key while you click the selected points and it will cycle through the different options.
If you get creative, you can modify basic shapes easily, but you can also get a feel for using the pen tool more easily if you have trouble with Bezier curves.
Don't forget to experiment as much as you can and have fun with it!