I am an American who has been living in Moscow since 2003, so I am familiar with your situation I think. Just coming here on a tourist visa or home stay will only allow you to stay in Russia for three months. If you want to stay a year, you have to have an invitation from a business who can hire foreigners that is willing to hire you and then if they like you extend your work visa for another year. As far as I know that is the only way you can stay for more than three months.
If you like it here, (get married) then you can apply for residence. You can apply without marriage, but it is much harder to get residence.
I would recommend that you find a job first and get an invitation and work permit good for a year. Just how much Russian do you know? Moscow is considered a very expensive city, so unless you plan on living with your girlfriend of working for a private language school that provides residence, you will not have an easy time here finding an affordable place to live.
You have the education and specialized skills that are hard to find in Russia, you can get a wok visa good for 5 years I think. Anyway, you will need a job first, you just can not pop right over and expect to find work, then stay. There is talk of the Federal Migration service ending their quotas on work permits and residences, but as of now these quotas are still in place. Russia wants to increase its commercial output, so these quotas maybe done away with, but at the same time I read on one Russian news site that some in the duma want those getting work permits to know Russian. That is how it is here as far as visas go, always in an ever changing confusion. I have an article I wrote on Yahoo Contribute:  called Jobs for Native English Speakers in Russia and I will be writing another one soon on getting residence and registering as a private individual entrepreneur and working for yourself in Moscow. This is what I do and do pretty well. I have been here quite awhile and like it here, it is not perfect, Moscow is a big, crowded, dirty city. Corruption is bad, but I love the people here, Moscow is a fantastic city, but you have to be prepared for living here and how to deal with everything like registering with the police, medical care if needed and what not. I love it here, otherwise I would have left a long time ago.
I just noticed that you are from the Philippines, are you Filipino?
                    JD