Is there and if so, what is the teshuva process for breaking a Neder? Additionally, once the Neder is broken is it still in effect?
Violating a Neder does not void the Neder, it is still binding and forbidden to violate in the future. The Gemara discusses a Nazir who is warned twice "do not drink", "do not drink"; and thus incurs punishment for each separate violation. The initial violation does not exempt him from future liability. (In the particular case of Nazir, breaking the vow may require him to start over, begining a new count of 30 days, as described in the Chumash.)