Hi Ryan,
I'm probably not much older or more experienced than you in the grand scheme of things but I've managed to land a couple of studio jobs before and have managed to stay off the coffee machine for a living for a while now, so a couple of tips that have helped me and might help you...
What do you look for in a potential employee?
Most employers probably look for a self starter. You have to be able to see a job that needs doing and just do it without being asked. Also, in this day and age, if it's a recording studio job you're going for, there has to be the potential for you to bring work to the studio. If you're not already in bands and meeting bands... get cracking!
Do you like to see their previous work with a resume?
The last two audio related jobs I've had the employers didn't even look at my resume. It's probably more about being personable. Realistically at this stage of your career (mine too), nothing you can show them that you've done will be a blip on their radar, so showreels are not always impressive to protential employers. It can't hurt to have a clear, concise and well presented resume and portfolio just in case though!
Do you look for someone who still needs some training?
I reckon I learned more about sound and how to work in a studio in the first week I worked for Rick than in the three years I studied sound. It's like learning to drive. You'll improve 10 fold the day Mum's not sitting in the passenger seat. Even if you don't think you need training, you do, so probably don't worry about it. In fact, if you can pick the employer, sometimes it's better to not even mention you went to audio school. It rubs some people the wrong way. IN FACT, if you are polite, intelligent, good at sound engineering and you smell OK, they'll probably presume you didn't go to audio school!
Do you prefer an email or to meet in person when someone is asking you for a job?
Depends on the person, but a phone call goes a long way. During my brief stint at Turtlerock I saw countless blanket emails "To the studio owner" who hadn't even bothered to find out the owners name. Seeing as there are litterally hundreds of audio students graduating every year I reckon you have to do better than that. An even better idea would be to meet the person by bringing a job to their studio. Main thing though is to be persistant. If you want a job somewhere, don't let them forget you're around. Not to the point of being a pest, but just a gentle poke every now and then so that.
Most of all, don't let anyone tell you it can't be done because you're young or because "the industry is dying". Trust me, it can be done. I'm doing it. Heaps of my good friends are doing it. My bands are doing it. All of my friends bands are doing it. You just have to try really hard and try not to be a dick to anyone who doesn't deserve it.