In terms of cofounder matching, I know that there will always be more non-technical people than technical people. In a sense they have their pick of the lot. So then what do technical cofounders look for in a non-technical cofounder? What experiences, assets (i.e. cash, connections, etc) and personality traits do you look for?
Business Development and Marketing strategy, Fundraising skill, skill of Managing people
As a technical founder who has been in ventures that have fallen apart because of non technical founders I have a bit of insight. Your founder should be focused on success. Not to make a masterpiece, not to hold onto their precious idea no matter what. If they are opportunistic, crafty and able to change and compromise without sentimentality your chance of success will be much greater. Just remember - your start up is a rocket. You must get to space with the fuel you have, or you plunge down to earth and die in a fireball. That means you have to do whatever you can to succeed. Don't let your ego get in the way. I've been involved in startups that have fallen apart over petty squabbles over small amounts of money and responsibilities.
Great answers here by everybody but I loved Craig's below .Very pertinent and inclusive of the thoughts I would have wanted to express.
I would want to add that the way I see it is that, the partitions should not be strictly technical & non-technical - yes indeed these are indeed the 2 umbrella roles that will be there in a startup.
But in order to make a Startup succeed , the folks with the startup will have to have a solid understanding of the "actual problem" that they are trying to address, how pervasive is this "solution need to the problem", to their target customer segments? are the launches being timed right ? are the solutions being priced right? are you building the right customer relationships for business continuity? are the first steps towards creating a brand identity progressing in the right direction? so that the awareness spread from this exercise is helping new customer acquisitions.
So Technologists will definitely persevere and focus on constructing the right solution and then we need people who will be able to address the above which will really make the difference of whether building the "solution" is really worth it.
But these folks (whom we want to bucket as non-technical) and focus on the so called business aspects of a startup and solve the above questions for you also need to (as Craig correctly points out below from his own expertise) need to have an understanding & appreciation on the technical aspects too.
As these folks need to be able to influence and guide the directional progress of the tech. engine to build products and services which really "solve a problem" which is "really very important" to real folks (target customers) who "are willing to pay" otherwise the startups will just burn money building something that will not in the future result in "revenue earning , profitable portfolio" for the Startup.
I would suggest you to for someone who can work for a hybrid role. Someone who knows business well and can understand technology inside out. If your startup is based on technology he can help you with that, and when your organization is growing he can help you with the Strategy and Organizational development. It actually depends on the current operations of your startup and what is your vision for next 5 to 10 years. Remember, if you never want to hire a person who would be stagnant for you after a year or two. We as consultants find this a very common reason as to why organizations are not growing. You can contact me if you need help with that.
I would look at their previous visible/verifiable results, not only the things he/she will bring to the company.
My career has been exactly that. I am non-technical in the sense that I am not a coder or an engineer, but I am a "business technologist" - I understand the application of technology, I know the 'art of the possible', I am passionate about technology's role in business and I am comfortable talking to the guys & girls that make the magic happen.
In essence I feel that the role is acting as a universal translator. Being someone who can translate the business need to the tech teams and interpreting the information coming back as to how/when/why/if a challenge can be resolved.
Growing a business, hitting glass ceilings, organisationally structuring well, expansion internationally, thinking about customer needs, etc are all areas that are easy to ignore if the company is primarily a bunch of really talented coders building the best in breed technology. You can have the best tech in the world, but failing to address the operational realities of running a business will only lead to one thing.