If your doctor suspects diverticulitis, then the best test to diagnose this is with a CT scan. You will probably also drink some oral contrast and receive some contrast via an IV prior to the CT scan.
After a first episode of diverticulitis, you will generally receive antibiotics (oral or IV) as well as bowel rest to allow the acute infection to subside. Depending on the severity of the infection, you may or may not be admitted to the hospital. Once your pain starts to subside, you will be placed on a low-residue diet.
After a one-time attack, patients do not generally need surgery unless they are below the age of 50. If you have recurrent attacks of diverticulitis, then a surgeon will recommend surgery to prevent further recurrences.
If you develop an abscess inside your abdomen from diverticulitis, you may need to have a radiologist drain the abscess with a needle.