I have 3 small steps going outside of my house. The patio ground, made of
cement, is painted blue. The paint has faded,and I'd like to repaint.

Part of the cement is cracked. The part that is cracked is in an akward
spot. It's just where the step is level to going a little up, if that makes
sense. If you were walking down the steps and kicked the heel of your show
to the very back of the step, it is that area that is cracked.

I've patched interior walls in my house but never patched cement. Sometimes
in very small spots, I'll just use my index finger since a brush is too big.
This area is also very small.

What type of cement should I use to patch? Is any special type of brush
needed, or just smooth it out with a finger? Suggestions appreciated!

Part of the cement is cracked. The part that is cracked is in an akward
spot. It's just where the step is level to going a little up, if that
makes sense. If you were walking down the steps and kicked the heel of
your show to the very back of the step, it is that area that is cracked.
I've patched interior walls in my house but never patched cement.
Sometimes in very small spots, I'll just use my index finger since a brush
is too big. This area is also very small. What type of cement should I use
to patch? Is any special type of brush needed, or just smooth it out with
a finger? Suggestions appreciated!

Your local hardware has cement patching compound. Just mix with water and
trowel it in, or use a putty knife. If compound is portland cement based,
keep the area damp after applying, by covering with saran wrap, or the like.
If it is acylic based, just let it dry.
If the crack is small and not of any structural consequence, you can use an
acrylic cement patching liquid that comes in a caulking cartridge, ready to
use. It sets up flexible. Works best only on flat cracks, not on vertical
surfaces, as it runs,.