After graduating from the University of Texas at San Antonio in 2011, Bobby Hoyt had $40,000 of student debt.

He didn't begin paying down his tab immediately, but he made up lost ground by buckling down and contributing 75% of his paycheck toward his loans starting in August 2012. Eighteen months after his initial payment, the high school band director was completely debt-free.

For anyone trying to dig their way out of the red, a good first step actually has nothing to do with your outstanding debt, according to Hoyt, who is now a full-time financial blogger. Before making any big payments, build an emergency fund, he encourages.

While Hoyt didn't take this first step — he immediately started directing the majority of his paycheck toward his debt, and used the rest of his income to live on — it's what he would advise his younger self to do.

"I was making these huge payments and I didn't have any cash saved up," he tells CNBC. "I was throwing all of my money at these loans, and if I had gotten hurt or sick, or if my car had broken down, I would've been screwed."

A couple of months into Hoyt's payment process, he shifted his focus to building up his rainy day fund. During this time period — November 2012 to February 2013 — he made minimum payments on his loans.

"I spent the next three months stashing money into my savings so that I could protect myself against any financial emergencies that might come up," he writes on his blog. "You need to have some money set aside. I put away about $3,000 during that time span that I didn't make consistent loan payments. This is something that I highly recommend you do before you start destroying your loans like I was about to do."

Personal-finance expert Dave Ramsey also recommends starting an emergency fund before tackling debt. The idea is that if an emergency or unexpected big cost arises, you won't have to go into more debt to cover it.

Aim to save $1,000 right away, Ramsey says.

Of course, $1,000 isn't an ideal amount to have in your emergency fund, but it acts as a sufficient temporary fund until you're debt-free.

Once you've paid off your debt, you can start building a more complete rainy day fund to cover the expert-recommended three to six months of living expenses.

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