I went to put on the hot water boiler heat for the first time and got no heat from my gas-powered boiler (I have water baseboard heating). What I did get was water dripping from a pipe that is open on the bottom with a bell-shaped valve on top, and now there is water all over the floor. Do you have any troubleshooting tips for a non-home-savvy person?

It sounds like the boiler's pressure-relief valve is opening (also known as a temperature pressure or TP valve). This valve is designed to open up if the pressure in the boiler exceeds 30 pounds. Typically, a boiler in a two-story home will operate at about 15 pounds. If your boiler is operating at 30, there is a problem and it could be dangerous.
There are other causes, too, like a waterlogged expansion tank (if you have an older home, these are common). Bottom line, this is NOT a do-it-yourself project and you would be best off calling a service contractor to diagnose and fix the problem. You should be doing this anyway to get the system serviced for all. All gas-, oil- and propane-fueled heating systems should be professionally serviced about now to make sure that they are operating safely and efficiently.
Answer by: Tom Kraeutler