Ink from a biro in the chest pocket
Short answer: Put a cloth under the fabric and dab the ink out with surgical spirit or hand sanitiser. Change the cloth often so the colour moves out rather than around.
Why ink behaves differently
Ink is dye dissolved in a solvent, not oil or protein. Water alone does not touch it, while alcohol dissolves it again. That is why a bottle of surgical spirit matters more than detergent in this particular case.
The method
Lay a clean white cloth under the stain. Put spirit on a cotton bud and dab from the edge inwards. The ink travels down into the cloth beneath. Move the cloth as soon as colour appears on it, or you simply spread the stain.
Afterwards
When no more colour lifts, rinse the area with cold water and wash with ordinary detergent. Do not dry the garment before you have seen the result in dry fabric, because ink can resurface. See bamboo shirts for men.
What to avoid
Do not rub, do not use hairspray, which often leaves a grease mark, and avoid warm water. A large ink stain in thin fabric rarely comes fully clean, but it can fade enough for wear at home. See bamboo t-shirts for men and bamboo clothing for men.
Frequently asked questions
Does milk work on ink
It is an old tip with limited effect. Spirit works far better and faster.
Can gel pen ink be removed
Harder, because the colour is thicker. The same method works but takes more rounds.
Should I use acetone
No. Acetone can dissolve elastane in the fabric and leave a hole.