In What Order Should You Pay Off Your Credit Cards? What is The Quickest Way To Pay Them Off?

Imagine a scenario where you have 2 credit cards. Both of them have a balance but one has a high APR of 25% while the other one with an APR of 10%. You should probably try to pay off the credit card that has a high APR. Since it has a high APR, you are going to be spending a lot of money on the interest rate and financial charges.
This is probably not a fixed strategy though. It depends upon the balance that you are holding on the different credit cards. If the balance on the credit card with the high APR is less then you will are likely to end up paying more in interest on the other card even though it has a low APR. If the balance on the high APR credit card is more than the other card then you should pay of the high APR card first to avoid the extra finance charges.
At the same time you should keep meeting the minimum payments on the other credit card with the low APR while making more than the minimum payment on the credit card that you are trying to pay off. As the balance reduces on this card so will the minimum payment but keep paying the same amount anyway. This will end your debt faster. Once that credit card is paid off, switch the amount that you were paying to that credit card to the next one. Add the amount that you were paying to the minimum payment that you were making.
There is an exception to the rule of paying off the credit card with the highest balance first. If you are going through a rough financial time you may find it hard to make the payment on the card that has the highest balance since it will also have the highest minimum amount.  What you can do here is to start by paying off the credit card that has the least amount of balance on it.  Make the minimum payment on all credit cards except the one with the lowest balance.  As you were doing earlier with the credit card with the highest APR make more than minimum payment on this card up to as much as you can afford.  Once this card is paid off work your way up successively to credit card with higher balances.  Allocate the amount that you would paying on to credit card that has been paid off in addition to the minimum payment that you were already making on that card.  When you finish paying off the second card as well work your way up to the third successive card allocating the total money from the payment from the first and second credit card along with the minimum payment you were already making on the third credit card.
What this process ensures is that you start with the credit card that will be the easiest and quickest to pay off. Starting with the lowest balance and working your way up means that as you move to tackling credit cards with a higher balance you automatically have more money available to you since you have paid off the credit cards with lower balances already.  By the time you reach the credit card with the highest balance you will have the money available from all the credit cards you have paid before that to tackle this large amount.
This theory is contrary to what you are normally told.  Attacking the credit card with the highest interest rate of the highest balance does not always make sense.  If you cannot tackle the high amount of debt just yet follow this practice by starting to pay off the lower balances first and you will find that paying off the large credit card balance becomes easier.

All in all which credit card you should be first depends on your financial conditions.  You will need to sit down and make a few basic calculations regarding how much of money and you can allocate to paying off your credit card debt.  You will also need to calculate how you can save the maximum amount of interest and other financial charges.  Basically which credit card you need to tackle first depends on how much cash you have to spare and the best way you can distributed amongst various credit card payments in order to reduce interest and financial charges.