A great way to get your foot in the door with a company is to be a temporary assistant. You fill in for people if they are sick, on vacation, or on maternity leave. The assignments can last for a day or two to even a couple of months. The best part is, there are a ton of temp agencies and anyone can apply. I had zero connections in Hollywood, so this is how I got my start.
The #1 rule of temping is you're not supposed to ask for jobs or try to get employment on your own to honor the relationship and introduction your agent forged with the company you're at. Your agent is supposed to be the go-between should a company want to hire you so they can collect a fee for "discovering" and "delivering" you to said company. This is how they make their money. Temp agencies help companies find temporary talent, do all the legwork, take care of the screening process, and issue the paychecks. And usually a company that has worked with the same temp repeatedly will want to hire them permanently.
Straight out of college, I joined the temp pool while I was job hunting. I got assigned to the desk of a VP while someone was out on maternity leave. One day, I noticed one of my co-workers bringing in a lot of people. I wasn't that close to her so I didn't know why. After a couple of days, I kept noticing she was still walking people through. I eventually got up the nerve to ask her who all these people were and she mentioned she was leaving the company and needed to find a replacement.
At that point, I had seen her bring in at least 5-7 people and figured they weren't finding the right person. I mentioned I'd love to be considered as I was temping and the regular assistant would return. My co-worker was extremely apologetic and said she would have totally considered me, but she thought I was already an employee and not a temp.
So with her help, she submitted me and had my temp agency contacted to say I was being considered. I did get hired and it all worked out in the end. I thought I'd get in trouble for what I did, but it turns out everyone was really happy and pleased!
I worked for the Chairman/CEO and finding someone to replace me to work for a VP wasn't hard at all. Because I had been at the company for awhile, I had already worked with the people who were my new bosses so it was a really smooth transition. Me speaking up saved them from a longer, more difficult search.
Before you break the rules, you should understand them and why they are in place. The goal is to act in a MUTUALLY-BENEFICIAL manner so everyone wins. Work the situation in your favor as delicately as possible without pissing anyone off in the process.