Since December 8th, the process to ensure that a marriage was celebrated validly has become quicker and more simple. Pope Francis announced the changes in September and has now confirmed that they are underway.
Further, Pope Francis has asked the Roman Rota, which is in charge of the process, to ensure that they always judge the cases for free. But he also mentioned that "the faithful who can afford it have a moral obligation to give an offering to causes for the poor.”
There is some confusion about the process of nullifying a marriage compared to receiving a divorce. They're not the same. The Catholic Church considers a marriage null only if some essential element of the matrimonial agreement is missing. An example would be a forced marriage.
September 27, 2015
"The Motu Proprio speeds up the procedures, but it is not divorce, because a sacramental marriage is indissoluble. This is not something the Church can change. It is doctrine; as a sacrament, marriage is indissoluble. The legal process for establishing that what seemed to be a sacrament was not, because of lack of freedom, for example, or lack of maturity, or mental illness…”
Other aspects of the new law include shortening the process and letting a bishop provide direct judgment for cases with a clear outcome. Further, going forward, completing the process once is enough. In the past it had to be repeated to become valid.