Summarize:

Whether inside or outside, you'll need to get your puppy used to the fact that you won't be around all the time. You can practice indoors by leaving your puppy in one room and leaving for a few minutes, then returning. Then begin putting the dog outside for short periods of time, one to five minutes to start. You need to accept that the dog will probably cry and make a fuss while it is outside.  Only leave a dog outside if you have a safe and secured fenced-in area. You must train the dog that nothing good will happen when they cry.  Only let the puppy in when it is quiet and (preferably) lying quietly. If you give in and go out with the dog or allow it to return inside when it is whining, then you are giving positive reinforcement to the unwanted behavior. Leave your puppy with a distraction, like a Kong toy stuffed with wet food, to keep them occupied and to help them associate the yard with positive things. This is a big key to training a dog. Once an allotted amount of time is up (remember to start with small time increments), go outside and praise the dog profusely with attention and petting. Maybe even give the pup a treat. The dog will eventually make a connection that if it is quiet and well behaved outside, it will be rewarded for that behavior. Continue the training by lengthening the time outside until the dog remains quiet outdoors for at least an hour (as long as the weather is nice). Now the dog should be able to better deal with the separation anxiety when left outside or alone. Hopefully the pup will just quiet down and take a nap instead. Make sure the puppy always has fresh water available. There are calming products available to help puppies with being alone. For instance, the dog appeasing pheromone (D.A.P.) has been shown to calm puppies in dog obedience classes. These come in collars, sprays, wipes or diffusers.
Practice letting the puppy be alone. Give your dog praise for good behavior. Slowly increase the puppy's alone time. Consider use of a calming product.