I have a baby dragon who has a  *  beside her colour. Does this mean she has inherited a deviant colour? 

That is indeed what that means :) Congratulations!

Well, to be precise, it means the baby has a Deviant Colour OR Deviant Pattern mutation, the * could be both. However, looking at your baby and its parents, it's safe to say it will be a Colour mutation, so it will look like this grown up: 

Thank you! Also, I'm not sure how she got it when neither of the parents are deviant. Is it random?

Yup, deviancy is random, to be exact, there's a 10% chance your pet will be one, if they meet the requirement. (Stated in the FAQ, Genetics and Breeding questions #6)

Now I understand. Thanks for all the answers, everyone!

I also have a baby that has the color tiger* i have researched her completely and she has a red (star) in both the dominant and recessive sides of her genetics chart. neither of her parents were Homogyns. I read the breeding guide. It said you have the best chance of getting a deviant that way. 

Does this mean that the female who gave birth to her have the possibility of giving birth to more diviants if bred to males that are homogyn with the red color.?

Depends on what you mean; it would increase the chance of your baby being homogenous, which would increase the number of potential deviants, but it won't increase the chance that be baby is deviant. -- Example(Metaphor); pretty much, think of it as rolling a dice, with each homogenous baby you get 1 roll.