Pretty new to the EE game here, just playing around with Arduinos and such, so please excuse me if this sounds a bit amateurish. I have a 3.7V LiPo battery, and I was just wondering if I could just hook it up to 5V vcc to charge it. I also have a 3.3v regulator, would it be better to pass it through that first?
No. Connecting a 3.7 V lithium cell to 5 V would damage the battery.
In electronics we have things called datasheets, which are provided by the manufacturer of devices to tell you exactly what these devices can do and what you must not do to them. The datasheet for your battery should tell you how the battery can be charged. You have to assume that anything outside of what the datasheet allows would be bad for the battery. In the case of a lithium battery, exploding and causing your house to burn down are not out of the question.
GO READ THE DATASHEET.
Lithium Ion and Lithium Polymer batteries require a Constant current / Constant voltage charge regime.
They can be spectacularly pyrotechnic if the cell terminal voltage exceeds 4.2V (amongst other things)
Single cells and stack sold commercially in most countries have safety features, but anyone who watches the tech. news has seen instances of these catching fire.
I would most certainly not just hook up a Li+ / LiPo battery to an uncontrolled power source at 5V.