It will help your vet a great deal if you are able to test and observe these behaviours before visiting the clinic.
Even if the signs are classic for separation anxiety, there could be an underlying medical problem that is causing your dog's stress level to rise.
Once medical conditions have been ruled out, behavioural therapy can be initiated.
Another way you can train your dog is to "practice" leaving the house.
Remember, whatever you are attempting to teach your dog, whether they are a puppy or an old mutt, the two "P" words are the most important - patience and praise.