Water-Based Ink Stains
Lay the stained clothing on top of a clean dry towel or cloth. Apply water to the stained area and blot with another clean cloth. While you blot, the stain will begin to transfer onto the cleaning cloth. Apply a small amount of liquid laundry detergent onto the ink stain and allow the fabric to sit for between 3-5 minutes.
Before drying, check to make sure the entire stain was removed. If any trace of the stained area remains, repeat the steps above. Drying the stained area before everything is removed will make it nearly impossible to remove later.
Permanent Ink Stains
Permanent ink is a very difficult stain to remove. If the fabric is able to be bleached, there might be a shot at removing the ink. Other than that, the following tips may help to at least fade the stain.
The first suggested step is to try rubbing alcohol. Grab a clean white towel and put the stained item on top. I always recommend testing any solution on a hidden seam of the fabric. After testing, blot the stained are with rubbing alcohol. The towel underneath may start to be wet and discolored from the ink leaching out. Try moving the garment to a clean dry section of the towel as this happens to keep from picking back up any of the removed ink. Continue until no more can be removed. Make sure you rinse the stained area completely free of the rubbing alcohol. Rinsing multiple times may be necessary.
My next suggestion, if rubbing alcohol does not work, is to try fingernail polish remover. Be warned that this stuff is heavy duty. There is a chance that it will damage the fabric. Be sure to test what happens on an inner seam or a hidden area of the clothing. Blot in the same way as you did with the rubbing alcohol. Be sure to move the stained area to a clean dry section of a towel as the ink stain is removed. Don't forget to rinse the rubbing alcohol completely from the fabric.
As a last resort, you can try acetone, although this can destroy a lot of fabric types. Do not use acetone on acetate and rayon fabrics. Always test first on a hidden seam. Place the stained fabric on a clean dry cloth and blot with acetone. Don't forget to thoroughly rinse the acetone from the fabric.
Ballpoint Ink Stains
If water-based stains are easy to remove and permanent ink stains are nearly impossible, ballpoint stains fall right in the middle. Just like in the examples above, start by laying your stained fabric on top of a clean dry cloth. Dab rubbing alcohol onto the ink stain. Begin blotting with a clean cloth. Continue until no ink stain remains. Rinse the clothing thoroughly. Now apply normal liquid laundry detergent onto the area and let it sit for between 3-5 minutes. Wash in the hottest water that is safe for the fabric.
If rubbing alcohol doesn't work, try nail polish remover, following the same instructions above. Be sure to rinse the fabric completely between using rubbing alcohol and nail polish remover. These items shouldn't be mixed.
Before drying, make sure the stain is completely gone. If it is not, repeat the previous steps until the stain is removed, or you decided to call it quits.