Your options are fairly limited because an employer is free to hire or not hire someone, as long as it is not for an illegal reason.  Hiring someone because they are a friend is not an illegal reason.  If this was the only reason for the hire, then you don't have many remedies.Your question is a little confusing in that it implies that you started training, but lost your position after the supervisor hire someone else.  Depending on how you were hired (i.e. if you had a contract, you were induced to leave another job for this position and then lost it), you may have some limited contractual type remedies.  You may also be able to file for unemployment.If you lost your employment or were denied a position for an illegal reason, then you could have a discrimination or retaliation suit.  For example, if they fired you or did not promote you because you were female, then that would be for an illegal reason.  If you were discriminated against in an employment context, you could file a complaint with the EEOC.If you think that there could be an illegal reason for the denial of the position, then arrange for a consultation with an employment law attorney and see if the specific facts of your case would qualify for one of the types of lawsuits described above.