There are several approaches to systemically eliminating debt.
The first method is to pay off the credit card with highest interest rate first.
Mathematically this debt solution makes the most sense in the long run because you reduce the total amount of interest paid and you get out of debt faster.
People with discipline should use this method.
The second approach is to pay off the credit card with the smallest balance first then apply that monthly payment to the next debt in addition to any extra amount that you can afford.
This debt solution is sometimes referred to as "snowball method".
You may have heard of this solution as it is taught by Dave Ramsey.
With this approach you first list all debts, excluding mortgage payments.
List the smallest balance first, then the second smallest balance until all are listed.
Now begin to eliminate debt by paying off the loan with the smallest balance first.
Once that is paid off, start paying off the second loan by adding the payment amount from the first loan to the payment amount of the second loan, plus any extra money that can be applied.
Repeat the process until all debts are paid.
There is a psychological benefit as well getting your debt paid down.
A person or family just feels better knowing that they have successfully eliminated a debt and that helps keep a person motivated.
By the time you get down to your last debts, the amount you can pay will have become much larger, similar to a "snowball" gaining momentum as it rolls down the hill packing on the snow.
The last approach is for those who are completely overwhelmed.
Find a reputable company to help eliminate debts or at least reduce debt by lowering the payment amounts.
Be wary of claims that debt can be settled for 60 or 70 %.