There can be certain indications of cancer in blood work, like an elevated white blood cell count, among others However, Drs usually don't screen for all the markers unless they have reason to, meaning, if you are just getting a check-up and are in otherwise good health, it is unlikely they ran all the screens for cancer. I was diagnosed with stage II breast cancer last year, and even after my diagnosis I had no markers in my blood work.
The main warning signs of cancer are the following (obviously, you don't have to have all or even any of the symptoms to have cancer...but the following are common)
bone pain at nighttime
unexplained weight loss
unexplained bony fractures
endocrine abnormalities (cushing's syndrome, SIADH)
Usually what happens is that the doctor will note these symptoms, and it will go along with a specific complaint related to where the cancer may be. For example, a person may be having any of the symptoms above and also be experiencing chest pain, hemoptysis or coughing. This raises questions of lung cancer...at this point the doctor will do imaging and biochemical investigations to see if (s)he can find evidence of a tumour. After this, a biopsy of the tumour must be taken and evaluated by a pathologist to see if it is malignant or not. If it is malignant, depending on the tissue type, the doctor will refer the patient on to oncology and they will decide if they need surgery and/or radiation and/or chemotherapy.
stones, trouble urinating, urinary obstruction, hydronephrosis (back up of urine in to the kidney), infections, hematuria (blood in the urine), pyelonephritis (inflammation due to infection of the kidney and renal pelvis), pain on urination etc.