The simplest way to pay off your debts without coming up short is to "wall them off." What do I mean? Simple: you need to build into your budget a set amount for repaying your debts, then stick to it, even as your income goes up and as your debts decrease.
Basically, the process goes like this. First, find the total minimum sum required to pay all of your outstanding debts as of this moment. When you have determined this sum, that is the amount you must pay each month to keep your debts in good standing. Note this figure and make it the "debt repayment" portion of your budget.
As time goes by, your debts will slowly decrease, and some of your debts - such as credit card debts - will gradually require smaller monthly minimum payments. However, your debt repayment budget must not decrease with them; it must remain fixed at the initial amount you calculated it to be when you began this process.
This is what I mean by "wall off your debts." By establishing at this point in time the minimum amount required to keep your debts current, you simultaneously established the amount required every month thereafter. Doing this creates a "known expense" in your budget, a set amount you know you will have to pay each month. The utility of doing things in this manner is psychological - you are removing the stress of unknown payment amounts by creating a fixed cost while also ensuring that they remain paid up. All of the guesswork is eliminated as well as the added expense of missed payments.
Meanwhile, as some of your debts decrease their monthly minimum amounts required for payment, you will end up with a left over amount of money out of your fixed monthly amount allocated to debts. Use this surplus to make an extra payment to whichever account would at that time lead to a lower monthly obligation the next month. Typically, this will be a credit card, though it could be something like a mortgage with primary mortgage insurance attached that can be gotten rid of once a mortgage is paid down to 80% of the loan-to-value ratio of the home it is on. This part will require that you do a comparative analysis of your existing debt accounts and the effect of extra payments made specifically to lower their monthly minimums. The purpose of this is to create a larger remainder of your fixed debt repayment amount such that you can "snowball" your debt repayments, gradually increasing the amount paid of your fixed total to individual debts as others decrease and disappear.
Continue this process until all of your debts are gone, while also being careful not to create new debts. If your income increases, you could increase the amount you allocate to paying debts, but you don't necessarily have to. If you've walled off your debts, they're gradually being taken care of faster and faster as the difference between your starting amount and the monthly minimum payments increases anyway, so you might as well put your increased income into savings, investments, or use it for your own enjoyment. This method is definitely not the fastest or most cost effective means of getting rid of your debts, but it is a method that can accomplish this while giving you comfort, peace of mind, and the means to have a life while ridding yourself of debt.