How to publish a paper? Being a software engineer for the most part of my life I have absolutley no idea how to start with publishing an "academic" kind of paper. During my latest research I've found an interesting algorithm for the task I've been solving (related to some calculations on financial markets). It's not some great result but I think it can be interesting for people doing the similar tasks and I'd like to publish it. 

I'm of course familar with a style of research papers since I use them extensivly at my job (thanks to Google Scholar and all the good people out there) and I'm able to google for free manuals on academic writing style and how to use LaTeX and I have a lot of friends mathematicians who will check my paper and help to make it look ok. 

But I have absolutely no idea what to do next! I don't belong to any academic institution or recognizable research entity, I work in a small local company, which will be happy to have its name on some paper published but this name will say nothing to anybody. I don't know anybody who is doing research in this area, I mean I've never communicated with anybody. 

How can I found the right place to send paper to? Do I need some sort of recommendation or review and how and where can I try to get them? What are my steps?.. I realize that all these are absolutely obvious things for you if you are a professional sceintist but I have no idea where to start :)
First, you should write up your result so it's comprehensible as you can make it, and send it to a journal. If your write-up looks like it is a real research paper, your paper should be sent out for review and possible publication. How to choose a journal? Look for other papers which are on roughly the same subject matter and around the same quality as yours, and see where they got published. 

Don't publish in a fourth-tier journal; if you do, it will never be read; these seem to exist only for the purpose of increasing the number of researcher's publications, and are not subscribed to by many academic libraries. To make sure you're not choosing one of these, check the online databases of a few good academic libraries, and make sure most of them subscribe to the journal you have picked.