Usually these are fairly simple - look where the cord enters the machine - if you can see a plastic cover usually held by a screw you'll be able to access the end of the cord and the switch. Have a look at the connections and decide if you want to have a go. Presumably the machine wasn't switched on when the dog decided to sharpen its teeth....!
howtomendit.com for free repair help, information and advice.
Try fixfault.com to fix vacuum cleaners.