For me (remember I work in the tech field, so this may not work for other jobs), I just spam monster and craigslist with resumes, anything linux, anything python, perl, mysql, postgres, soap, xmlrpc, interface design. Anything that i have a half way decent understanding of, to see what comes back.
When I get interview requests back I see 'what does this company do, what am I likely to be doing?'. I do a ton of research before the interview so i can make sure to check all the boxes, and I prepare for the interview questions I'm likely to get.
I'll use Rackspace as an example since it's where I work now:
Level 3 system admin: Requirements, BASH (Programming language), RedHat Certified Engineer (Operating system expert), MySQL exp+ (database backends), Python/Perl/Ruby a plus (likely going to be doing a bit of api consumption), Bachelors degree + 5 years experience (Not an entry level job, want intelligent veterans).
Preperation:
I'm already a BASH expert going in. Check.
I've never touched RedHat before, but I'm a debian expert. Research the differences and similarities between the 2 distros. 6-8 hours of prep and study. Check.
MySQL experience. I can develop stuff to use MySQL but never administered it. Light reading on Performance and Tuning to answer interview questions. Check.
Python/Perl/Ruby. I've been working in Perl for years, but I've never touched the others. These are usually done in order of importance. Read up on common interface Libraries for python and write some simple proof of concept code for reference. 6-10 hours. Check.
Education. This is the hard one. You're going to have to talk your ass off here if you're missing one or the other (in my case I was missing both). New paragraph for this one since it's the one that applies to you directly.
If you're lacking the experience for a job that you feel you can do well, don't let that put you off. First you need to write your resume to tell a story. I know there's a 1 page rule, but to be honest, you're not going to get a call back on a 1 pager straight out of college. You need to go into the things that make you enjoy the field you're in and be able to go into detail in your interview.
I don't know a lot about accounting so these examples might be silly. 'Ran my father's A/P department, generated checks and contracts with vendors. Negotiated rates, reductions, and payment schedules. My negotiations saved the company $3,000 of it's previous $38,000 in monthly vendor expenditures'.
Of course you probably won't be able to use that specific example, but I'm sure if you went to school for 4 years there's a reason you did it. Tell them what that reason was and why you'd be a benefit to their company.
If you get the you're overqualified bullshit, don't take it lying down. There are no allegiances when you're trying to get paid. Stuff like 'This will be my first job out of college. I'm ready to work hard for you right now. I've got student loans to pay and I'm willing to dedicate my time to you for our mutual gain. You're business will get an awesome reputation because of my extremely detailed work, and I'll be able to afford ramen and pay off my loans. This is a win win for both of us. Even if I do leave the company earlier than you'd like you can't afford to take me at the price I cost right now with no experience. I can fill a seat for you, make your clients happy, and enhance the brand with my education and dedication to my work and the success of the company.'
You have to be ready for that statement and you have to be ready with a come back for it. It can't feel rehearsed, you just have to know what your strengths are, and even if you're under-experienced, or over qualified, if you sell those strengths well, no hiring manager in his right mind will turn you away.
Mine for Rackspace was: "You're right I don't have a degree. I went to college for 2 years to become an English teacher. I'm well read, I'm well spoken, I think for myself and I think about the best way to solve problems. Outside of those things, what else does college buy me in this industry without the real world experience to back it up? I've been in this industry for a very short 4 years, but in those 4 years I've done some amazing things. I started as a Flash Developer for a small marketing company. I was just sitting in their call center making cold calls when suddenly they needed someone to help them with their web development effort. I told them I had done some Flash programming in high school, and they gave me a shot at the job. I didn't get a raise, I didn't get over time, I just got a shot. I spent 20 hours a day on that project for a month, and what came of it? I'd developed a dynamically generated inventory system based in flash, virtual test drive applications, written in flash, and a full rich media campaign ready to be started, in one month. I did all that for $10 an hour just to prove to myself I could do it.
After the project was over they got their deal, sold the campaign to the customer without management rights, so the job was over for me, but I decided right then, that I'd never had this love for literature, so I immersed myself in the technical world. I quit my job with the marketing company and took a job as a phone support rep for Verizon. Yeah, I was that guy. At Verizon I took my primary job very seriously. I destroyed their metric system, while I was on the clock, and while I was off the clock I optimized their ticket system integration with their internal systems, created a note taking system for phone calls that went global, and was promoted to an internal software developer. They eventually outsourced all of their call centers and I was out of a job again.
I then got a job as a low level tech at a hosting company. I started the job learned the ropes, and got to work doing what I do best. First I optimized my job by setting up their astrisk server and having it integrate into a web interface for their customer directory. When a customer called in, it would update a web page of recent calls with the customer's information so the tech taking the call could easily see all of the systems for the account. I created a 1 time use login token system for support techs to use that would keep the client's machine secure, but wouldn't require the tech to waste time looking for the password to help the customer immediately. For all of that work I got promoted to build tech. Put in 16 hour days as a build tech with an average turn around time of 45 minutes per system. You guys work in a hosting company, so as you can imagine that turn around time is unheard of in this industry.'
I had more than all of that above, but eventually at then end of this they double checked my stories with all of my references and I had an offer literally within 4 hours of my interview. My plane landed in dallas and I had the email with the offer letter by the time I made it home.
I was grossly under experienced and under qualified for the job, but I got it, and every job before that purely for the fact that I'm dedicated to doing good work. You give me an interesting project and I will take that thing to the moon and bake you cookies for the flight. You can't afford not to hire me. That's the sentiment you have to give people when you walk out of the interview room.
TL;DR: Research the company. Research the job requirements. Make them forget you're under-qualified by telling them why you are the best investment they could ever make. Make experience secondary and dedication your primary strength. Remember, you're selling yourself, don't be timid when they tell you that you don't meeting their experience requirements. Be ready for that and woo them.
Btw, I'm going on to my third promotion in 2 years at Rackspace. Believe me, my methods do work, but they can't be empty words.