This is a very simple tool that adds anchor points to a path.
However, it's often not necessary to do so. If you're using the Pen or Freeform Pen tool, if you click on an existing anchor, it will be removed.
You can create and save a Tool Preset for any tool. This will remember settings that you choose. Presets for brushes are much more useful than for some tools. If you wish to use presets, you have the option of either creating a tool preset or a brush preset. Right click on the Tool Presets button to reset the tool to default settings.
When you have an existing path, you can delete anchor points from it with this tool. However, if you are using the Pen Tool, Freeform Pen Tool or the Curvature Pen Tool, you can just click on an existing anchor to delete it. The cursor will indicate this, showing a - (minus) sign.
Select the Delete Anchor Point Tool. Like most tools it shares the button with other tools and the one that is visible, is the last used tool. All the tools on this button are Pen tools.
Click on the existing path to add an anchor point to the path.
You can't just click anywhere. You must click on a path.
Alternatively, if you are using the Pen Tool, Freeform Pen Tool or the Curvature Pen Tool, you can just click on the path to add an anchor point.
You will then often need to move the anchor point. There are different methods, depending on which Pen tool you're using.
You can select the Convert Point tool, then click on an anchor and drag it. Note that when you click on an anchor point with the Convert Point tool, it resets the handles.
If you are using the Curvature Pen Tool, you can just click on the path (which will add an anchor) and drag, or click on an existing anchor and drag.
If you are using the Pen Tool, or the Curvature Pen Tool you can press and hold the Ctrl key, then click and drag, either on the path itself or an anchor.
You can select the Delete Anchor Point Tool, but often it's not necessary to do so. If you're using the Pen or Freeform Pen tool, if you click on an existing anchor, it will be deleted.