Let's say you have 2 debts: A $2,000 car loan at 6% and an $11,000 credit card debt at 18%. While continuing to maintain minimum monthly payments on both, it makes mathematical sense to use any extra cash and apply this to the credit card debt since it has the higher interest rate. However, psychologically, it has been found to be easier if you apply any extra cash towards paying down the car loan since the balance is lower and you will see it paid off much sooner than the credit card debt. Once it is completely paid off you will feel good at having achieved one of your goals and encouraged to continue your journey of becoming debt free. You will then add the monthly payment amount you had used for the car loan and combine this with your credit card monthly payment, thus paying down the credit card balance at a much faster rate. Any extra cash you have will also be applied to pay down the credit card debt, with the result you will arrive at the finish line much more quickly than you realized.
Once both debts are completely paid off, keep making the same payments to yourself by creating an emergency fund, say of $1000-$2000. Resist the urge to spend this, and instead know that this will cover you for any possible emergencies that life may throw at you down the road. This will also help prevent you from going back into debt again.