With your printer, some of the fine lines dividing the cells may not be printing out. Every printer has its own idea of how thick a line should be. The Sudoku program recognizes this, so has an in-built means for getting thicker lines.
You can use the Appearance dialog to make the lines thicker. Press F2 to get the Appearance dialog, and go to the Line Weights tab. From the list of choices, select the kind of line you want to make thicker, and then adjust its thickness or "weight". You will see the changes being made in the on-screen puzzle grid.
Although the lines on the screen are thicker, there is another step to make sure that the lines print out the way you want them.
When you bring up the normal Print dialog, there is an "Appearance" frame in it (not the same thing as the Appearance dialog), with two radio boxes - one for "Onscreen settings" and one for "Printing.saf settings". The latter is the default. If you want to print out using the line-thickness you see on-screen, change the setting to "Onscreen settings".
When you leave the checkmark on the default "Printing.saf settings", printing is done using the settings in a special appearance file called Printing.saf.
To save yourself the bother of changing the on-screen line thickness every time you want to print a puzzle, you should *Save* the (corrected) onscreen settings into the Printing.saf file, for future use. The next time you go to print a puzzle, you can leave the Print dialog at its default "Printing.saf settings". You will get the printed puzzles the way you want them, without messing up the way your onscreen puzzle looks.
All of this is explained in the Help topics. Within the Sudoku program, go to the Help menu and select "Help Topics...". Then on the Index tab, select "Printing.saf/Appearance in print".