When Archie joined the family we were faced with an interesting problem. He was and is a sweet dog but having been tied outside he did not know how to behave indoors and had separation anxiety. He is not an only dog, or only pet for that matter (the cats and dogs all hang out) but he chewed and pulled up the carpet once we were gone.
Here are some of things we did to change this behavior:
1. Exercise Exercise Exercise
He was walked and or played with at least 30 mins a day. This was crucial, as he slept.
2. Teach basic commands of sit, stay.
He was taught basic obedience commands, sit, stay, come, leave it not just helped him understand what it meant to live indoors now but it gave him a sense that he belonged in the "pack." It became a game of sorts since the other dogs joined in to show how good they were at getting treats :) Having trained Kramer with a professional, it was easy to apply that knowledge to Archie.
3. Confine to only part of the house when alone.
We didn't crate Arch since that tended to make him more wound up, but if allowed to pace through the house all day just increased his anxiety. So a baby gate was used to confine him but he was placed in such a way so he could interact with everyone. Meaning he was not put in a back bedroom when the rest of the furry family hung out in the living room. So he still had company but not full run of the house.
4. Test on the weekends
We slowly allowed for time without baby gate confinement on the weekends. We would go to lunch for example and allow him to be with the others for the two hours or so we were gone, note this was always done after exercise. Slowly this time was increased, Archie got to learn our routine, while understanding that yes we came back; and his confidence grew.
5. We never used an anti bark collar or shock collar.
Given his gentle nature this would only have confused and stressed him.
6 Patience, patience, patience
There is no substitute for this, Arch never had a "real" family before so not only did he have to learn his place in the pack, he had to learn about the concept of a "pack." There were times we would make progress and then for some reason have to do a two steps back recheck :) Yelling, only increases the stress on the pet, and prolongs the sense of separation.
7. Use herbal remedies if needed
Early on in this process it may be necessary to use herbal remedies like Chamomile or Rescue Remedy to just east the anxiety.
Archie is now a well adjusted senior, and since Kramer's passing the man in charge :) he will still do things like get one of my tennis shoes and hang out with it if I am gone all day :) they are never chewed :)