Before touching the foot with the glass splinter, you should wash your hands with soap and warm water. Then, wash the foot with warm soapy water. You can use a clean cloth or paper towel for that part.
Next, make sure your tweezers and needle are clean. To do so, bring a small amount of water to a boil, then dip the ends of the tweezers and needle into the boiling water. Then, wipe them off with an alcohol pad (like the ones found in a first aid kit) or a cotton ball. The main thing to keep in mind is not introducing an infection into the broken skin from dirty tools. Keep them clean!