How do I get companies to sponsor my project?

You need to look at this from the company's point of view, the basic question they are asking is what is in it for them. They're not going to pay you to develop it and you keep hold of the copyright, or allow everyone else to use what they've paid for you to develop.

Also, they have no idea whether you'll actually deliver in six months, if you have a full time other job, there's a limit on what you can achieve part-time. If it were possible to create such a product working 6 months part-time, another company could do it in 2 months with 5 developers, i.e. the barrier to entry is low and you're subject to competition.

How much money are you going to tell the company they will make from the sponsorship (don't know is never an acceptable answer)?

Constructively, I suggest writing a brief business plan (you probably could get feedback on how to improve it by posting a link to it on this site) and iterate through until people who have their own business (like me) say yes, I like the sound of that.

A lot of people think open source is a very romantic idea, in practice very few domains are able to commercialize it. Companies know this, so think about that if part of your pitch is "it must be open source', they will ask detailed questions as to how they are going to make their money back.

Companies stay in business because they know how to make money (and not waste), so prepare yourself for brutal feedback (if you're not able to cope with this, keep it as a pet project). And remember the first idea you have in business is never the magic idea, it's takes several years of evolving the idea with commerical feedback before you make it, if ever...

Put yourself in the shoes of the company and ask "What's in it for me?"

When you can answer this question, you can think about selling sponsorship to the company.

Keeping in mind that many companies will spend 5-6 figure amounts on good software tools, you may be able to position your product as a conventional sale. If you can find 3 customers @ $10k each, you have your $30k. If the prototype is usable you may be able to sell the prototype with the promise of quick incremental upgrades -- perhaps they pay in stages, 1/13th of the sale amount every two weeks when you deliver your biweekly upgrade.

The open source angle may work too -- you can position the "community" as an extra support venue. It may also reduce the risk of buying from you in that they have access to source and improvements made by third parties in case anything happens to you (or you lose interest, or get a better job offer, or the product gets bought by a competitor, etc).

Either position you choose, remember to answer "What's in it for me?".

Interesting topic. There are a few consideration I want to add:

• it's important that you encourage participation to the project. I suggest you first of all to adopt a very commercial-friendly license (like Apache Software License or MIT or equivalent) that gives all the community of user the freedom to use the product in commercial and not-commercial offering

• it's important that you make clear since the beginning how the development process is structured and managed. Having the source code "open" is not enough, if you or your team are the only people allowed to commit code. It's equally important to have all the discussions between developers openly available in a mailing list, to make clear how 3rd party can submit code, and to explain how external developers can become part of the development team

• As for finding sponsors, you can prepare a simple ROI study explaining how much the project would cost to develop to a single company, and how 2-3 companies sponsoring the project would "split the bill" and have a better product, more tested and customizable

• Advertising can be a part of it (putting sponsors' logos in the project page), but ads are not that expensive! I would focus more on the advantages of having a complete software available for 1/3 of its development costs

To add to the other answers, the "what's in it for me" for a company could be the inclusion of features that suit them more than other users. For instance they need to output all their data in a certain XML format. You include that feature, even though there are more urgent feature requests. (I.e. if they relied on completely free open source development process the feature they need would not be added for years.)

As another example, if it is a scripting language you can get Oracle to sponsor it by making sure you include an Oracle database binding, and using an Oracle DB in all your tutorials. They'll be even happier (*) if you push work on other database bindings until after their paid sponsorship period ends. Product placement isn't just for the movies.

*: No slur on Oracle intended, just using them for example.