I am non EU citizen. I have a tourist visa for 3 months. I am now in Germany. My girlfriend is Swedish and we were living together for 1 year in UAE. She got an offer in Germany and she is moving to Germany next week. We love each other and we want to stay together in any way possible. How can I stay with her? Can we get married here and we stay together? Or can we apply to live as partners?
Getting married would be the most straightforward approach. :)
The traditional answer is that for most countries, for a visit of up to 90 days, you won't need a visa. Many countries have an agreement that allows you to stay for 90 days every six months in the Schengen area. If you want to stay there for longer than 90 days, and it's clear that you do, you will need a residency permit for a country in the Schengen area.
For Germany, at least as of 2010, you could do it when you are there on a tourist visa. There's a good walkthrough of the process at this site. A good rule of thumb for these things is to contact the local German Embassy before you leave. They can help walk you through the process.
One quick thought is that you could get a job-seeker's visa. That's six months (or at least it used to be in Germany), and the only thing you have to do is to prove that you can support yourself during that time.
Edit: It sounds like the job-seeker's visa is the best option for you right now. You have lots of options, especially since you appear to be multilingual! Welcome to the German adventure!
First read this official EU legal document: Right of Union citizens and their family members to move and reside freely within the territory of the Member States.
It means that if you're married or have a legal partnership with a citizen from another EU country (in this case Sweden) you have the right to stay in the EU country that is not your partner's country of origin.
The details can vary across EU country, but overall if you both want to live in a Schengen country and you can legally enter one Schengen country without a specific visa (or on a tourist visa) and you are married (or legal partnership) you can head to the country where you want to live (Germany in this case), and you both register. Your partner gets a normal EU resident permit, you will get a short term permit. You're not allowed to leave that country (Germany) for 6 months, and afterwards which you will get a 5 year resident permit with which you can travel freely through the EU.
Best to look up the details for Germany before starting the process.
And overall it often means that you have a lot more rights in EU countries that are not your partner's home country. In 3rd countries there can be no restrictions about things like income.