The short answer is as many as you like (and can afford). It is helpful to approach the first couple (I would recommend Sprint distance) as an introduction to the whole process of triathlons. It may help to volunteer at one if you have never been to one. Learn how to set up your transition area, get a feel for swimming with a group, know what it is like to go from swim to bike to run and how your body responds. Focus on one or two as "A" races that you build your training towards.Other races can be "B" or "C" races where you are concentrating on one or two aspects of the race but getting in training miles.
Don't be afraid to ask questions here. There are many helpful people, some coaches, and all of us were Newbies at one point. Good luck and have fun.
I did my first sprint last September and will be doing one in May. I entered in my age group. I came in 13 amoung the Newbies, first for my age group in the Newbies. I figure it's time to compete with my age group.