If a Jew is in debt and in the process of paying off the debt should the Jew be giving maaser? If it has been struggle just to pay necessities and an extra sum comes in to help, should the Jew give a maaser from this new sum or should he just use it to help pay off the things he needs to pay and to help with necessities and then give a maaser when all his debts are paid?

Shalom, The question of how to give ma'aser money (that is 10% of one's earnings given to charity) is a good one. In general, many Rabbis are of the opinion that giving 10% of one's earnings to charity is a custom and not a binding halacha. That being said, it is certainly a strong custom that one should try hard to fulfill - but because it is only a custom, the exact guidelines of how to calculate the exact sum are not as strict as many other halachot. Someone struggling financially, and all the more so if they are in debt, is exempt from giving 10% to charity (see Tshuvot VeHanhagot - Rav Sternboch shlitah - 1,560). This applies to those in financial need and living without luxuries at all. If such a person was given some money "to help", then they should use all the money given to them for the purpose it was given, that is to help out their monetary situation. If it was money that came in with no particular earmarking - i.e. you received a birthday gift or bonus etc - then even though one normally does give ma'aser on such money, one should first use it to pay off debts and buy necessities, before starting to calculate 10% for charity. May you be blessed with a healthy income.