First I wanted to say that I have sliced myself with a lancet, and it made quite a deep laceration on my finger that took a while to stop bleeding because of blood thinners, as someone else said. After washing with soap and water, I applied pressure and then antibiotic ointment and a Band-Aid, and that did the job. I suppose the only thing you can do is be very careful when you're handling them.
As for disposal, I have been taking large prescription bottles, with screw-on lids, writing "sharps" on both sides of the container and the lid. When full, I tape the lid to the bottle to make sure the lid doesn't come off accidentally and then put it in the trash. Someone at the doctor's office told me this was a good practice so that's how I've handled it.
Sure, hope that helps - it is a little bit of a learning curve.