I have left PolePup already, but he isnt the least bit phased by it as we have PoleDog, so hes not actually alone. I am now building up to taking them out for a bit separately, so that PolePup does get used to being alone, and the fact that sometimes they can`t always be together.
With some of the fosters I have had with severe separation anxiety, and with my own dogs as pups I have started by making sure they are 100% confident, settled and happy in the house, and doing lots and lots of confidence building.
I also do this before I do any socialisation too, as I really do not feel that throwing a dog in at the deep end when they are scared of water and expecting them to swim is a good idea. As a very respected trainer once said to me, one bad experience negates a hundred good ones, build confidence first so that they have something to fall back on.
In my experience, they do bounce back better from negative experiences if you have taken the time to build their confidence first.
Then I would take them out in the car to the petrol station, so that they could see me get out, get petrol and then go in and pay for the petrol. I would do this a once every three days or so, and then go to a corner shop and nip in for a newspaper with them left in the car.
Gradually I would up the time left alone in the car (in appropriate weather of course!) until they were happy for 30 minutes, always leaving an old t shirt of mine with them.
Next I would try it in the house, so go outside to get the mail/prune a bush/just stand around outside a window where they could see me for five mins. Do that a few times, then I would be outside for five mins where they couldn`t see me, and gradually build up the time that way.
I also always use a cue, so I say "back in a minute" so that they don`t suddenly realise that I am not there, which was a huge issue for some of my fosters.