Tekes is Finnish government organization that can be a significant source of public funding for finnish startups. Their official english language description is "Finnish funding agency for technology and innovation". They shell out about half a billion EUR of money yearly for all sorts of R&D funding, market research funding, etc. That's is tied to the finnish governments share of EU governed funding, and as a general rule the money cannot be used to fund activities that would somehow distort competition; like using it to fund sales activities directly.
As you might know I'm a member of two Tekes "boards" or "management committees" or what ever would be the proper english language term for those. The first one is the Verso technology program. Which is a Tekes programme for funding Vertical Software Solutions; emphasis on the games industry, social media, web applications, b2b web, social software etc. Verso is somewhat sizeable; up to 120M EUR of funding. The second one is the user driven research projects board, that is meant to review and steer innovation policy on key research. Members are from the finnish Ministry of Economy, VTT (technical research centre of Finland), and other key institutions and universities.
Besides seeing the administrative "insides" of Tekes I have also applied for about 10+ Tekes projects for my companies over the years. Most recently Dopplr, Muxlim and RunToShop.

CC Attribution: Twit2art@Flickr
There are a few things you should know about applying financing from Tekes. Please note that these are my own opinions and cannot be taken as official advice or instructions from Tekes despite my board memberships.
1) Always book a meeting to intro your project. The success rate of getting your project funded is about 70% at the moment, but getting it funded exactly as you applied it is far less likely than that. Tekes people see a lot of applications, for a lot of random ideas and projects. Always make the call, talk to them, book a meeting and explain what you and the project are about.
2) Take their free advice. Tekes people can often tell you exactly how the project is most likely to receive funding: out of some technology programme? As an R&D project? As a loan, or maybe as a grant? etc.
3) Prepare your application well. Be honest. Fill out the application the best you can. Put in all the annexes they asked for, possibly more (management team CVs, business plan, slides of your latest presentation etc). Tekes has a system that not many know about: the person you have met regarding your idea will need to present that idea up for funding internally in their closed meetings. So it is your job to make your case as presentable and attractive as possible for someone else to present convincingly and get it right. If your contact person "gets it wrong" due to your incomplete materials you may end up with a negative decision, or getting half the money you applied for.
4) After sending in everything, followup. Call them, ask for stuff that needs to be complemented or clarified. Suggest and take a followup meeting to go through the application and its annexes if necessary. Your contact person is going to have to represent you in their internal decision making, do what you can to help her.
5) What ever decision you get, it's usually final. It is quite rare to see a decision altered, so what ever you get can be pretty much considered final. If you feel the urge to complain a lot; consider that you may be in a situation where you are applying for another project some time in the future, so don't over do it and stick to the facts etc.
6) Once the project starts, keep a good log. You will need to log accounts separately for the project, save every RFQ, every quotation you received on 3rd party work, have all the people keep taps on their hours done for the project, etc. Tekes will provide you with instructions, I suggest you follow them. There is a chance that you will end up in a list projects that gets reviewed and inspected later by Tekes hired accountants. If that happens you will end up spending a day or two in a conference room explaining to accountants all the receipts and costs associated with the project - at that moment you better have them available. This has happened to me, and I learned a lot in the process ;) it is a bit like a government tax audit. If you are super "lucky" you will get an European Union -level audition done to your project. Only a handful of projects every year get that, but it is possible. Then you will be talking to an accountant who has flown in from France, Spain or Italy to check your receipts =)

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7) When the project is completed, plan the followup. All projects end sooner or later. Follow Tekes instructions on how to report them. After filing in the report it takes them a few weeks up to 90 days to process it and get you your money. Possibly longer if it was a loan instead of a grant (this is because loans go through the State Treasury instead of Tekes). Once done, you need to plan your followup. Is everything really done and there's nothing left for your company besides to conquer the world and laugh (like Joker) all the way to the bank? If not quite so yet, then plan your next project, and start presenting its idea to Tekes people early on. It is good stuff for them if you get some continuity going and do multiple projects with increasingly good results. That's precisely what they would love to see as a result of the funding activities.
8) And lastly: get help. Applying for Tekes funding can be complicated (depending on the project). As a startup it can take significant amount of your time and attention as a manager. I suggest getting help. Some good "helpers" out there include: