What methods should I use to encourage and train my puppy not to bark and whine?

I have recently adopted a 5 month old staffy lab cross who is extremely adorable. Sadly she's had a traumatic start in life and I am her 3rd owner since she was born! I have been giving her lots of love and reassurance. We play lots and walk at least twice a day. She is cage trained and fantastic on and off the lead and plays very well with other dogs. I discovered the other day when I popped out from a very miffed neighbour that's she barked and cried at a very high pitched level! Not ideal in an echoy terraced house! Looking it up on the internet I think she maybe suffering from separation anxiety issues. Understandable given her start in life. I want to nip this in the bud as quickly as possible so can anyone please advise on methods they have successfully used?