A foreign body in the skin is most commonly a sliver of some material. Most of the time it is a wood splinter that goes in just very slightly under the skin.
If the sliver is a piece of pencil lead, remember that what is called "pencil lead" is not really lead. It is actually graphite, which is harmless. Even colored pencil leads are nontoxic.
Most slivers can be removed with a needle and tweezers. These items can be sterilized with alcohol or a flame. The skin surrounding the sliver should also be washed with soap before you try to remove the sliver. Use the needle to expose fully the end of the sliver. Then grasp the sliver firmly with the tweezers and pull it out at the same angle that it went in. Getting a good grip the first time is especially important with slivers that go in perpendicular to the skin or those trapped under a fingernail.
A horizontal sliver just under the skin's surface (where you can see all of it) can be removed by opening the skin along the length of the sliver and flicking it out. If these type of slivers are numerous and pain-free, they can be left in. Eventually they will come out with normal shedding of the skin.
Usually cactus spines break when pressure is applied with tweezers. The following method can be used for removing cactus spines, as well as small fiberglass spicules or plant stickers (for example, stinging nettle): Apply a layer of facial gel or wax depilatory (hair remover). Let it air-dry for 5 minutes, or speed up the process with a hair dryer. Then peel off the gel or wax with the spicules. You can also try white glue, but it is less effective.