How to get switched and constant power combo on an outlet
You are on the right track. As it comes from the store, the upper and lower sections of standard double outlets are connected by the small tab connecting the brass plates under the screws on either side.

To separate those sections so that one half is constantly on and the other half is switched, break the tab on the hot side of the outlet. This is usually the side with brass screws. The other, neutral side usually has silver screws. You can be sure on modern outlets because the side with the larger slot is the neutral. In your first picture, the neutral is on the right.

Break the tab on the hot side by grasping it with the tip of a needle-nose pliers and flexing front to back until it snaps off. Do not break off the tab on the neutral side (that would be removed only if the two halves were going to be fed by different breakers; not your case).

You should have two hot wires, one always on and one switched. They may both be black or one black and one red, or even one white, but with a black marking. Attach the always on wire to the brass screw next to the half you want always on. The other should be attached to the brass screw next to the half you want switched.

The neutral (white) wire is attached to either screw on the silver side. The remaining tab carries that connection to both halves.