Select the parent part.

Click Create → Point parts ... to open the Feature Panel for Point Parts.

Make the cursor tool visible.

Move the cursor to the desired spot. (Interactively or by using the Transformation Editor.)

and

Click the Add Point (at cursor) button. (Repeat as many times as needed)

OR

Click the Load points from file... button. (Which will bring up the file select dialog) and select a file that contains the desired points.

(See Point Part File Format)

A simple sample of a Point Part file:

#Version 1.0
#EnSight Point Format
-.5,  -.5,   .5
-.5,   .5,   .6
 .5,  -.5,   .7
 .5,   .5,   .4
-1.5, -1.5,  .5
1.5,   1.5,  .3
2.25,  2.1,  1.5

Click Create with selected parts.

To create a mesh from a point part, click on the Advanced button.