There are a handful of these, and most of them aren’t canon which is to say they weren’t developed in the manga. The ones that are canon include: “Wood Dragon”, “Eagle” (symbolizing Heavenly Punishment), and two secret hand gestures known solely by those with the Mangekyo Sharingan.
A fan’s website for Naruto, My Anime List, has this quote from Jiraiya:
“One particular use of Shadow Clones is in conjunction with Secret Hand Gestures.” So whether or not there are more canonical hand signs used by ninja characters hasn’t been confirmed yet since it appears that only one character has ever made use of a secret hand gesture at any point in the series.
What we do know about these hand signs is that they are gestures of respect and reverence for certain people, places, and ideas. To perform a secret hand gesture is to give your greatest possible compliment, offer faith in one’s abilities (or potential), or show undying gratitude for someone’s teachings. If the person performing the hand sign is not near an appropriate place or person to perform it in front of then he or she may simply make the gesture into empty air.
The basic rule to using them is that you cannot give a secret hand sign toward yourself and nobody else can use them toward you. Doing either of these would be considered extremely disgraceful and dishonorable.