Having some extra cash is helpful when the world falls apart. But emergency funds, while great in theory, are very difficult to put into practice. That is why so few people get around to saving one - most people have more urgent financial demands.
However, one should learn how to multitask with your money, moving between short- and long-term priorities.
Write down your expenses from the past few months (look at your debit and credit card bills, your bank statements, etc.)
Next, see what is essential to support your basic needs and what you can cut if you had to.
Calculate the minimum amount you could survive on if things got tight, then multiply that amount by three. That is your starting goal for your emergency fund.
Eventually you'll want to save enough to live on for three to six months if you had to.
Try to transfer your debt onto a zero-interest credit card (also known as a balance-transfer card). It will give you a limited time window where your debt won't accrue interest and allow you to get rid of your debt faster. But ensure you can pay it off within that window, otherwise the interest rate will skyrocket again.
Once the debt is gone, put that same amount of money toward your emergency fund instead.
Some people are disciplined enough to manually set aside "leftover" money at the end of every month into a high-interest savings account. Others take the decision-making out of the equation and automate the entire process. Most banks have a feature that allows you to set up recurring transfers from your checking account into your savings account.
Saving up three to six months' worth of expenses could take years. That's fine. Just keep at it.