No wireless internet, should I get a router?

Hello,

I live in an apartment and I do not have a wireless connection to internet, so I use the ethernet cable for my MacbookPro. It is inconvenient because I can't use the internet anywhere else in my apartment other than my room. So is getting a router a good idea? I heard that if I get one and connect the router with the ethernet cord, I will get an wireless access to internet in certain area limit? Is that true? If it is true, would my neighbors be able to use my internet (I don't want that to happen..)? How does a router exactly work? And if I do get a router, could you please recommend me a good one, yet affordable?

Thank you.