An oscilloscope will be able to show you the signal from a signal generator and how the signal is modified by the amplifier. It will not tell you if the amplifier is working properly, this will left to your interpretation of the signal (a big distinction, as hooking it up is the easy part).
You generally connect the signal generator on the input and the oscilloscope on the output but if you have a faulty amplifier you may probe other locations within the amplifier (amplification stages, power supply output, voltage rails). To test the amplifier easily and at high volume it's recommend you use a suitable dummy load on the speaker outputs in place of the speaker (has other testing advantages as well).
A 1kHz sine wave is often used as a test frequency. You will need to understand how impedance works for making correct measurements, the rating of your oscilloscope and also how floating and non floating circuits work, e.g. inadvertently grounding circuits with your test equipment that are sitting at a voltage potential higher than the earth ground on your oscilloscope. So important to understand the input and output specifications of your test equipment.
While you may be able to get a general idea of the amplifiers operation, accurate noise and distortion measurements may require additional test equipment such as a distortion analyzer and spectrum analyzer. A multimeter is another essential tool, two of them for tube amplifier repairs.
As the amplifier needs to be turned on to amplify, putting your hands inside an amplifier that runs on mains power is a safety risk (hundreds of volts). It's recommended that you start learning safety aspects of working on equipment first before tackling anything else. Read this whole chapter on safety.
http://www.allaboutcircuits.com/textbook/direct-current/chpt-3/importance-electrical-safety/Then you need to learn how to use your oscilloscope and other test equipment, and how to manipulate the amp to get a clean signal for testing and then how to interpret different types of distortion and other problems plus learn how to confirm if your amplifiers performance is within spec, a science unto itself.
If somethings wrong, you need to learn how to repair amplifiers.