Oscilloscope Tutorial

I just got a DSO Nano Oscilloscope and I’m having trouble figuring out how to use it properly. I have a project where I’m looking at the output of a current transformer. The output is a sine wave (if I’m monitoring a resistive load) and it’s about can go up to 1/3 volt. I want to build a little op-amp amplifier and increase the voltage by 10x, then I want to smooth it out so it’s close to DC. I’m trying to use my DSO Nano to see if I’m building the op amp circuit right (I’m new to designing electronic circuits). There’s little things I’m not sure of, like do I hook up one lead or two from the oscilloscope? I can get a waveform if I hook up one lead and sometimes it goes away when I hook up two. I also get waveforms with nothing hooked up, I don’t know if the DSO is too close to wires or something. When I put a voltmeter on my circuit, I got a much different voltage then the DSO was displaying. Also the DSO was telling me the RMS voltage of my circuit was bigger then the peak-peak, which didn’t seem right. Anyway, I think I have a lot to learn with this and I’m looking for a good resource that can explain the basics. Any suggestions?