For the last few months I have been doing a great deal of reading and research about Islam, listening to lectures, and reading through a couple translations of Qur'an. From an intellectual/rational capacity it all makes sense to me. Learning about Islam feels like coming home after a long absence. But I don't really know what it means or what it's like to believe in God. How do you know if you believe in God, or how do you learn to believe?
There is no god but God. Muhammad is the messenger of God. (Shahada)
If you believe that you actually believe in what you said, then you're a believer.
Other definition could be -
This world is a prison for the believer and paradise for the non-believer. (Muslim)
For sure there forms and levels of hypocrisy, e.g. Qur'an 4:142, you should check them out.
Allah knows the best.