Well now the plot thickens... depends on what kind of recorder you have on hand. Usually the output from the amp is going to be rated at a given wattage, which may be far in excess of what your recorder is capable of tolerating. Now from your latest statement, I gather that you have plugged your guitar into the input of your recorder directly and were able to record the product. If that is the case, you can pretty much be assured that the recorder is looking for a fairly low power source (as your pickups generate a fairly weak output signal, similar to what you might get from a small recording microphone). Feed it something around 59 volts at 10 watts + and something is going to make smoke.
For Recording an electric guitar, you would usually just Mic the speaker and rock on from there. There is a reference document on the Shure website that has guidelines for doing that effectively. Here's the catch though, now you have to buy a mic. If your amp has a line level output, you can generally send that directly to a recording device because the output is tapped out of the circuit after the pre-amp stage and before the power amp stage. It would still be nice to have some sort of output limiter on that anyway for the safety of your recorder. When in doubt, always check the specs of the equipment to make sure that the output of one device doesn't exceed the input limits of the other.
I had an old electronics teacher that insisted that everything electrical had "smoke" in it.... if we screwed up, we didn't burn it up, but just let the "smoke" out of it. Nothing beats the sound of popping capacitors and the smell of ozone first thing in the morning!