Help with a RF reciever circuit
Your schematic does resemble a basic radio receiver, but the whole thing is a lot more complicated than that. The LC circuit needs to be tunable, the choice of transistor is an important one (as well as correctly biasing it), that resistor should probably be on the collector side, you'd need something on the output to indicate what kind of signal is present, etc... And you do need equipment for measuring oscillations, unless you hope to come up with a working configuration of parts by accident. Or at least you'd need to thoroughly simulate the circuit before there's any point in building it.

If you really want to build your own radio receiver, you'll need to know a lot about filters and amplifier circuits... Or follow detailed plans that someone has made, with detailed component values and all; I'm sure you can find some with a bit of googling :-)