Salaam all:
I am very new to Islam, in fact, it has only been about a month since I decided to become a Muslim. What made me 'convert' is for a few different reasons. A show that aired in 2005-2006 made me curious about Islam, though I had been curious about it before in the past but didn't do any research at the time. After 9/11 the view of Muslims certainly changed yet a part of me always felt the terrorists who flew plans into the Twin Towers and attempted to do the same at other locations in the US, i never felt they represented the truth of Islam. I just didn't look much into it at the time.
However, the series I mentioned, made me want to know more. I bought an English translation of the Holy Qur'an. I knew I could download it online but I wanted the book, so I could read it anywhere in the house, not just at my computer. I don't own a laptop and the Qur'an was much cheaper than buying a laptop
It did not take long before I realized Islam isn't what I originally thought it was. It made more sense to me and felt more....for lack of better word, 'natural' to me as the correct path for me. Allah is the one true God and no others should be worshiped instead or with him. None are equal. The holy Trinity of Christianity is putting others on the same level as Allah.
It is very good you are not converting to Islam solely to marry your girlfriend. If you don't truly embrace it, there will always be frictions, especially if she's very devout. You have to embrace Islam for yourself and truly wish to do so from your heart, not just to win the 'girl' so to speak. Allah knows what is truly in your heart, there is no hiding from Him.
As I am so very new as a Muslim, I have a huge amount of things to learn myself... one good move I made was reaching to my local Muslim community. A simple google search revealed to me there was a website for the local Mosque which had a list of contact persons. I emailed one and expressed my interest in learning about Islam and possibly converting. He was very helpful, even if what he did was ask if he could forward my email to another in the community who knew Islam far better than he. This person was very helpful and very warm and open, made me feel very welcome and gave a fantastic impression of the Muslim community. It was a way for me to learn more about the religion and he told me of a monthly potluck held at the Mosque, which he invited me to attend. I did, and it was a most interesting experience. I also learned not to rush to learn everything in record time, as Islam is a bottomless font of information...even those who had lifetimes studying, being Muslim don't know everything.
In Summary, I suggest reading an English translation of the Holy Qur'an, and since your girlfriend is Muslim, grill her with questions. Borrow her Qur'an if it is in English. Or whatever language you are most comfortable with. Speaking on a newbie's point of view, reading the Holy Qur'an helped me see what Islam is...and understand its not a real complex religion, or is it a once a week prayer. It has challenges, many which I am working on still, such as performing all the required prayers...I am not a morning person. Then there is just learning the prayers themselves, then the format/stages etc. but take everything one step at a time. Several Muslims I have met so far and various resources i found online, have said think of Islam like a ladder, take it one rung at a time, don't race to the top. Otherwise, if you miss your step you may end up at the bottom (ie lose your way).
Youtube has many wonderful videos, including various 'how to pray' videos. I also really enjoy 'Towards Understanding Surah Yusuf' (a chapter in the Qur'an. English translations may have Yusuf as 'Joseph', which mine does) by Yasir Qadhi. It is in 20 parts each about 25 min long. Very interesting.