In describing bringing home a rescue animal, someone wrote "he's [the dog] is still trying to figure out whether or not you are going to eat him."
A bit dramatic but it is a good analogy. Your new family member knows nothing about you. And while you know your home is a thousand times better than living in a shelter, your new companion doesn't know that yet. Just coming into a new environment can be scary. So for the first couple of days with your new family member, do nothing.
No walks (except potty breaks), no visitors, no pet stores, no baths, no hand feeding, no playing with food, etc.. Just put food down and walk away.
No petting unless the dog specifically asks for petting. And when he/she asks, just calm, short pets - maybe on the chest or or under the chin. Pet only for a few seconds, stop, see if he wants you to continue. No hugging squeezing, no vigorous rubbing. No physical playing.
Don't give full run of the house yet. Maybe just access to the family room and the master bedroom (if dog is allowed in there) then slowly increase freedom.
A vet trip might be necessary of course, but wait for everything else.
Keep pup out of trouble - remote controls, shoes out of reach; counters clean; etc..
It can be tempting to introduce you new family member to friends and family but it's too early for that. Let the new dog/cat/.. get you know you and your immediate in-residence family first.
After a few days you can start short walks in quiet places. Do not stop and talk and strangers, don't walk near strangers or other dogs. It's too soon for the dog park yet.
After a few more days, family and friends can start meeting your dog, but just one person at a time and make sure the person is well coached. No petting at first - unless the dog specifically asks for it and then only short pets.
If you know that a friend or family member won't listen to your instructions or if you know the person has used a "heavy hand" with dogs before, then hold off on those meetings.
All of the above is just for "normal" dogs or dogs who appear to be normal. If your pup already has known issues, then you'd want to go much much slower than what I describe here.
For more on bringing home a rescue dog, check out Patricia McConnell's "Love Has No Age Limit"
only 100 pages but full of good info.