The typical tests for gastrointestinal complaints vary according to the symptoms you're experiencing. Most people have the following done:
1) Blood work - including CBC (complete blood count), CMP (comprehensive metabolic panel), TSH (thyroid-stimulating hormone)
2) Stool tests checking for: ova and parasites, fecal leukocytes, and fecal occult blood; perhaps a stool culture as well; and possibly a urinalysis
3) Sigmoidoscopy, colonoscopy, and/or EGD (esophogastroduodenoscopy - say that ten times fast), which are relatively simple outpatient procedures where you get scoped and biopsied.
Some people also have radiological studies like an abdominal CT or small bowel follow-through, also known as a barium swallow.
Bacterial overgrowth tends to be discovered using a very simple breath test.