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Thai Pete's answer is close but there is actually a lot of politics involved between Hayes and Hatsumi. Hayes' brand of ninjutsu is based on Hatsumi's earlier teachings before the Bujinkan was formed.

No matter where you decide to train you should always do your homework on the school and compare it to what else is available. Finding a great teacher is a lot more important than finding a particular style.

One more note, I've met a couple Bujinkan instructors from my area and it sounds like most legit instructors have made at least a couple visits to Hatsumi's hombu, (I could be wrong on the name there) or main school.

You can learn Ninjutsu from an early age - a lot of the Ryu (schools) are family systems where they start training children early.

You need to be careful selecting a school. There are a lot of schools that don't have a lineage and just use the term to gain business.

The best bet is to look at a Bujinkan School. It is headed by Masaaki Hatsumi out of Japan, but with representatives here in the US. Most notably Stephen K. Hayes. He has been a staple in the Ninjutsu world for decades, and only one of a few to study with the Master in Japan. He is well respected in the field.

Check his site listed below, and you may find a school near you.