As soon as you notice that your dog has ticks you remove them
You do not allow the ticks to remain on your dog... depending on how many there are he/she could become anemic.
Some ticks carry Lyme disease as well as carry other diseases.
Yes the ticks could also get on you, you just simply remove them, as for lice, some forms of these little parasites also can get on humans.
Here is a link about ticks....pictures, FAQ's and how to remove
http://www.dogsandticks.com/
ADD:::
Of course ticks get on humans
Ticks stay attached until you either remove them properly
or until they have drank enough blood to the point that their bodies swell and they drop off.
Here is a link for identifying ticks http://www.oes.org/html/how_2_identify_different_ticks.html
Link for removing a tick http://firstaid.about.com/od/bitesstings/ht/06_TickRemoval.htm