Clicker train your pup to limp with this training video. This is a video on how to teach your dog to limp using the clicker training method.
The old school way of training this behavior was to grab your dogs paw, restraining it while you walk forwards, and continue to do this until your dog doesn't put down their foot. Another way I saw in a book was to have your dog on a lead with their choke chain on, and loop it around their foot, so in order for the pain to be released on their neck, they had to raise their paw.
So INSTEAD, using the clicker training method, I will show you how to get your dog to figure it out all on their own! Not only is training like this fun for you and your dog, it is both mentally challenging for you and your dog. I can bet you that if you attempt this trick your dog will be taking a LOOONNNGGG nap afterwards! Mental stimulation is just as good at tiring out a dog as physical stimulation.
Keep sessions very short (3 min) and fun, it should take quite a few sessions on each of the steps to get the final behavior down, unless you have a three legged dog.