Some dogs simply don't, or won't learn how to beg or "sit pretty" on their haunches. The best way to figure out whether to skip teaching this trick is to have your dog sit, grab both paws and lift them up. If the dog's hind end stays seated instead of jumping up for even a few seconds, your dog can probably learn to beg fairly easily. Trainers agree that a motivated dog can learn to beg even if it is uncomfortable for them, but it may take much more time and effort.
The conventional method for training this trick is holding a piece of food above the dog's head as he is sitting. If this doesn't work, or she keeps jumping up, try this method:
Alternative Method
Forget the "beg". Teach your dog to shake (already know it? great), then teach him "other paw". (It's almost as easy as teaching shake originally) Randomly have your "dog sit", "shake", "other paw" when you get treats out.
At some point, when the dog has this routine drilled into him, sit him down and say "beg". He will get excited and in frustration he will eventually lift one paw and then lift the "other paw" before putting the first down. If you are clicker training, this is the moment to click. If you are training with traditional methods, the brief moment that both paws are off the ground treat and praise, praise, praise saying "good beg, good beg".
When your dog realizes that the movement of having both paws off the ground is what you are asking for, he'll begin to lift both paws at the command "beg". This is the rough beginning of a finished "beg". To polish the trick, just withhold the treat until the dog stays up a bit longer than the last time. Most dogs will need to learn to stay up slowly- it's not an easy trick, physically, for most dogs- especially large ones. They will need to develop muscles not usually used and improve their balance. Once your dog knows beg means to stay seated, tt may help to push the treat back farther over the head to help the dog understand you want it to go up all the way. With practice, your dog should be able to hold this pose for anywhere from several seconds to minutes.