Fretting

I am a complete beginner. I just picked up my first guitar yesterday and have been trying to play some chords like C, D, E... and I've been looking on the Internet for help. I guess my question is, are you pressing down on the string hard with your fretting fingers or just resting on the strings when playing cords? Thanks in advance.

You press down hard enough so that the strings don't buzz.
How hard you press will depend on the type of guitar and guage of strings you're using.

How hard you push down will also affect the pitch a little.

Try and keep your fingers pressed down close to the fret bars.

I have an Alvarez RF8, it is a beginning guitar. I have what i believe to be medium gauge strings. Thank you for your help.

Well, if you don't press down hard with your fingers and just keep them resting on the strings then you will only mute and muffle the notes, and you will end up only hearing the open string notes.
When playing a chord like C (and I'm guessing you are playing it on a position lower down the frets) then you should press down hard enough so that the string is touching both frets at either side of your finger, and your fingertip just about touching the fretboard. You should hear a clear note. Do this with all the fingers and make sure they do not touch (even slightly) the strings you are not ment to be fretting.

I hope that makes it simpler to understand.

Your fingers will hurt at first, but soon they'll start to harden.

The best thing you can probably do is getting a teacher. He/she will answer any question you have and guide you properly through the great and mystic journey of playing a guitar.

And practice, practice, get naked and then practice!

Yes, i can feel the pain in my fingers. I'll keep practicing.

Yes an 8 gauge or a 9 gauge set of strings will make it easier to play - extra light or light.