How do I find out my vocal range? Maybe I could sing into a chromatic tuner and see how low and high I can go? Would that work?

Something I noticed: I find it easier to sing on tune to System Of A Down songs (Which are in Drop C tuning), and I definately CAN'T sing Master of puppets. My voice is higher than the original vocals. This may sound newbish but how can I sing on tune to songs which are in a lower tuning than songs which are in standard?

P.S: I am new to singing, be patient with me.

I'm not a singer but I do like to test my vocal range and such because I find it imperative to getting music inside of your head and becoming a well rounded musician. I match the pitch of my voice to the pitch on the instrument and find what is easy for me to reach and what isn't. For example my talking voice is about a G.

As for the system of a down and metallica songs. It all depends on what key your voice is most comfortable singing in. Like master of puppets is in E minor so your voice must not be well suited for that key. I don't know system of a down very well but you say that they are in drop C so I assume that they are in C minor so your voice must have a vocal range that is well suited for that key.
That's a rather "dirty" method, but I guess it can give a general idea? There's so much more to finding your range than just "notes you can hit". It's about timbre as well.

Also often people tend to take falsetto into account, where as it is not really counted as being in your REAL range.

A teacher/coach would be best to tell you.. but working with a piano can give you an idea. Just be aware of falsetto. No one has 4 octave ranges like you sometimes hear people claiming in quick and dirty vocal finding guides.