Changing batteries:
To replace the button-cells, unscrew (to the left) the rear cap. Inside is a spring and the light assembly. The LED assembly can be unscrewed from the light assembly, leaving an opening through which the cells or cell sleeve can be removed and replaced. The first cell will probably be easy to remove. The other two will probably need to be coaxed out with toothpicks or the like (don't use anything metal, as it can short the minus side to the case) through the two slots on opposite sides of the cell compartment. Maybe a small diameter magnet will be helpful.
Once you've removed the old cells, you can place the new cells on a flat surface, side by side, with the minus side up (the + or flatter side down) and put the cell compartment (or sleeve if it came out) over a cell and block that cell from falling out as you place it over the next cell until you have all three cells in the tube (or plastic sleeve, in which case push the loaded sleeve into the tube with its slots aligned with those in the tube). Turning the tube open end up, you will need to push the cells in far enough to expose the threads inside the end. Now you can screw in the LED assembly, being careful to start it straight. If it is hard to screw, or looks crooked, back off and retry. You can now push the on/off button in back to be sure it works. After you have the LED assembly screwed in tightly, you need to assemble the spring onto the end of the light assembly opposite the LED. You will probably be able to do this by pushing the spring against it while twisting the light assembly to the right, just like screwing it on. Now you can put the spring and light assembly into the end cap of the pen, and screw the cap onto the pen.