Early stomach cancer often does not cause clear symptoms.
Like with most cancers of internal your organs, symptoms mostly occur when the cancer is well-progressed, and therefore already difficult to treat.
You will undergo a lot of tests in order to make sure what is the cause of your symptoms. Your specialist will be a gastro-enterologist: a doctor who specializes in diagnosing and treating digestive problems.
The next step will be to take X-rays of your esophagus (the pipe between your throat and stomach) and stomach. You need to drink a "white blubber". It's a barium solution to make your stomach show up more clearly on the x-rays.
Around the same time you will have to do an endoscopy: it's a camera to look in your stomach with a tube (endoscope) through your mouth. Of course this all happens under local anesthesia.
During the endoscopy, doctors can remove "strange" tissue from your stomach and do a biopsy on it. The laboratory will check the tissue under a microscope for cancer cells.
Since the results will be send to a lab, you could gain some time doing the biopsy in a hospital that has its own lab.
A biopsy is the sure way to know if cancer cells are present or not.
Always consult your doctors and read more about stomach cancer symptoms!