Thank you for your question.
When you find a tick, you should get a pair of gloves, a clean pair of tweezers or a commercial tick remover, some antiseptic, and some rubbing alcohol in a container with a lid.
A tick remover is very handy because you just press it against your dog's skin, slide the notch under the tick, and it comes off.
After you have removed the tick, you should wipe the area with antiseptic. Then drop the tick in the rubbing alcohol to kill it. You may want to save the tick in case your dog gets sick. It can be tested for Lyme disease. Your dog's blood can also be tested for Lyme disease.
After removing the ticks, you should apply a tick preventative topical treatment, such as Frontline Plus or Advantix, or whatever product is recommended by your veterinarian. This will kill any remaining ticks that you may have missed.
Keep an eye on where the ticks were removed to be sure there is no sign of infection. If you see swelling or oozing, you should take your dog to the veterinarian.
And yes, ticks can fall off your dog and spread it to you. That is why it is important to be sure there are none on your dog and to use a tick preventative.