FORTUNE — Dear Annie: Since being pink-slipped from my job as a construction manager almost three years ago, I’ve been making ends meet with a string of low-skilled jobs that don’t really use my abilities and aren’t leading anywhere. I keep hearing that there are a lot of opportunities in high tech, and I’d love to go after a job in that field, but I have almost no formal tech training (although I enjoy fooling around with computers and have taught myself a couple of programming languages in my spare time). I did take a few computer science courses in college, but I never graduated.

So, I have two questions: Would I have to go back and finish college to get into IT? And, even if I somehow managed to do that, what are my chances of getting hired with no work experience as a techie? — Dead End Dan

Dear Dan: It’s certainly true that job opportunities are plentiful in high tech. Most in demand right now are people skilled in health care IT, security (both network and mobile), systems integration, and mobile app development. Then there’s the cloud. Help-wanted ads for cloud computing are up 61% over last year at this time, according to a new study by workforce-research firm Wanted Technologies.

Altogether, says Todd Thibodeaux, head of computer industry trade group CompTIA, about half a million IT jobs in the U.S. are going begging. One reason employers can’t find enough skilled hires, even with unemployment so high: a wide range of federal and state-funded grant programs are available to pay for tech training, yet most people who are eligible to apply (like you, perhaps) are unaware that the programs exist.

“It’s a huge problem,” says Thibodeaux. “Government agencies that administer these grants, at both the federal and state levels, need to do a much better job of getting the word out.”

In the meantime, anyone interested in looking into a training for a new career can find all the relevant information on a special Department of Labor web site.

The good news, from your point of view: You don’t need to go back to school for a bachelor’s degree. Many top IT training courses are offered by community colleges, by tech companies like Microsoft (MSFT), and by specialized computer training schools, online and in person. “To get started on a tech career, you don’t need anywhere near a four-year degree,” Thibodeaux says.

You might consider beginning with one of the basic certifications CompTIA offers (which, like most other legitimate training courses, are covered by government grants, if you qualify), such as the basic A+ certification. Employers look for these credentials. In one recent survey, 86% of IT hiring managers said certifications are “a high priority” in evaluating job candidates.

Complete descriptions of all CompTIA certifications, including a new one in cloud computing that launched just last month, are available on the association’s web site, along with aptitude tests to help you choose a specific career path. “You don’t have to be a math or science genius to succeed in IT,” Thibodeaux says. “But you do need problem-solving aptitude and interest — and, increasingly, good people skills.”

Let’s assume you have those. Your second question — whether you can get hired without work experience — is tougher. “Employers tend to prefer candidates with at least some experience,” notes Tom Silver, senior vice president for North America at tech job board Dice.com. However, he adds, the current talent crunch may work in your favor: “In order to address the skills shortage, companies may have to compromise on experience requirements. That might make it easier on entry-level job applicants.”

Take cloud computing, for instance. Researchers on the Wanted Technologies study found that about half of the additional job ads that were posted this year (compared to last year) stated that cloud experience is a must. The other half require training, but no experience.

Another area where newbies may find a welcome is Microsoft’s .NET, a platform for mobile app development. A recent Dice report notes that the platform is “an accessible entry point” for “novices looking to break into the tech industry.” Says Silver, “It’s a relatively straightforward framework to learn and, while recruiters often chase mid-career talent, almost one-third of .NET searches in our database call for less than three years of experience.”

Of course, even getting one or two years of experience may be a challenge. Three suggestions: First, tap your network. “If you know anyone in IT, friend them on Facebook, join their LinkedIn networks, and get connected to their contacts,” says Thibodeaux. “Only about 30% of IT jobs now are filled through advertised postings. The other 70% of the time, people are hiring people they know.”

Second, try temping. Once you have some training and a certification or two under your belt, companies like Manpower, Robert Half International, and Kelly IT Resources can help you find short-term, entry-level project work where you can build practical know-how and meet people.

And third, keep in mind that attitude counts. “Training and certifications are a great start,” says Michael Dsupin, CEO of Talener, a tech staffing company. “But more and more, our clients are looking for someone passionate, hungry, and enthusiastic.” The fact that you’ve been teaching yourself programming languages just for fun is a clear sign of genuine enthusiasm, so do talk about it: “Without actual work experience, it’s critical to discuss your tech hobbies.”

Dsupin tells a story you may appreciate, about what he calls “one of my favorite placements of all time.” A job applicant was trying to switch to a tech career from a different field, with a brand new Microsoft Certification and no experience. Confronted with a skeptical team of hiring managers, recalls Dsupin, “he said something like, ‘I know this certification means nothing. I want to learn and, given the opportunity, I will deliver.’”

He got the job.

Talkback: If you’re in IT, how did you get your first job? If you’re a tech hiring manager, would you hire someone with training but no experience? Leave a comment below.