There are many common signs such as: weight loss, loss of appetite, sores, bad odors, bleeding, swelling, and lameness.
We had a mixed breed dog when I was a child who had cancer. The dog developed tumors on its stomach that were large and quite visable. The dog also gained a lot of weight before finally losing it all before it passed. It never had any energy and just laid around all day.
I had a dog who had cancer. She was a half Chow half German Shephard. A tumor grew on her back and we thought it was an allergic reaction to something. It never went away and it got worse and worse. My parents took the dog to the vet and tests were run to find out what was going on. If your dog doesn't want to eat it's food or has a visible tumor or you can feel lumps when you pet it, then take it to the vet.
My Beagle died of cancer: I did not know he had it until he began sneezing one weekend and could not stop -- it was in his face, sinuses and had matasticized throughout his body.
also see Which Cancer Treatment for Dogs Is the Least Invasive?
also see When Warts May Indicate Canine Skin Cancer
also see Canine Cancer Treatment Options: A Brief Overview
also see Lung Cancers in Dogs