Shelley, H. Pylori is unusual in that it is a bacteria which lives in the stomach (the only one). Until a few years ago it was thought no bacteria could survive the acidity of the stomach but H. Pylori can. It is the bacteria which causes stomach ulcers. It is not a normal inhabitant of the body, and can be quite tricky to get rid of.
There is a blood test available which will test for antibodies, but it only tells you if you have had an infection in the past. A better test is a breath test which tests for a metabolite of the bacteria not normally present in human breath. It is very sensitive.
H. Pylori can be quite tricky to eradicate. The normal route is a course of Antibiotics . Ouch!
There are natural alternatives available - e.g. coconut oil, manuka honey, and mastic gum. This last one was recommend by someone at the ulcer forum (the closest thing curezone has to a h.pylori forum).
If you do a search you could probably find other natural remedies.