There are many different kinds of Production companies, but here's my advice (especially if you have little or no money):
1. Think of a company name.
2. This name is now another name for you. You own a solitary proprietorship: the simplest kind of business to run...no registration needed (except perhaps to copyright the name if you want). Now, buy equipment you need...find people to help you and make movies!
3. Label your movies with the company name...and wallah! a production company!!
4. IMPORTANT: get a website...a decent one...with your movies (or at least clips) on it...this is a crucial tool these days and is becoming very cheap!
http://Globat.com is the best value, but you have to know a lot about building websites!
http://Freewebs.com is a good free one, but it's slow.
5. Spread the word about your company by sending your movies to festivals (free or cheap ones at first), and also over the internet (at sites like this). If a print media is interested in covering your company too..awesome!!! but it happens more rarely.
NOTE: Don't expect to make money from your new company...at least not at first!
ALSO NOTE: There are all kinds of companies...you may want to form a large one..in which case you want to incorporate. There are companies that make commercials, wedding videos, JUST their own movies (like me), or all of the above...my steps are just what I did pretty much, and it's really been great for me.
ALSO NOTE AGAIN: It takes money to earn money, if your business has no budget, it won't for years. Once money comes in, it will get easier and easier to make money. Most good small companies that I know about earn no money, and are run as a hobby/passion of the owners (like mine). Keep your day job!
Check out my site:
http://LoganLProductions.com I put some money into it (not too much), but have earned about 5% back ever!