The Pen Tool (1) is the main tool you will be using when creating vector graphic. It can be used in two "modes" as I call them.
Here we will see what you can do in Paths Mode (2)

In Paths Mode everything you draw will become outlines. Have a look at the picture.
There are few variations of the Pen Tool (see top bar)

PEN TOOL itself (green) -
You can draw any shape or outline, you can trace any object in your image and then smooth it out using those direction lines and anchor points. The less anchor points you have the smoother your lines are.

FREEFORM PEN TOOL (pink) -
Use it just as well as you would use an ordinary brush or pencil . The only difference is that your drawing will still remain vector.

Rectangle, Ellipse, Lines, etc.. (blue) -
create any geometric shape using these, use them for frames, outlines,etc..

CUSTOM SHAPES TOOL (yellow)-
These are the easiest

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