Two Very Simple Questions about relays.

I am working with Arduino for the first time to power 12V LEDs in various combinations, turning on and off the lights from a Max patch. This is very basic stuff and there's plenty of threads with similar questions, but I just can't wrap my head around how to wire this up.

I've got several LEDs from a strip like this:

I understand that relays are the way to go to work with the 12V LEDs at the distance I need. I got this sainsmart relay:

I have no problem getting the relays to turn on with digital outs from my Uno; I hear the clicking of the relays and the correct light on the relay board lights up, which I take to mean the pathway is set. But perusing existing topics, I can't figure out the proper way to attach the LEDs to the relay outputs and provide them with power.

Into which slots of each individual relay outputs do I plug the positive and negative terminals of each LED strip? I keep seeing the phrase "common ground" thrown around, but I'm not sure how that works. How do I get the proper 12V into the relay board? I suspect it's through the inputs on the bottom of the board grouped GND, VOC, JD-VOC near the bottom of the board.

here's an example of what I have so far, which functionally turns the relays on and off but does nothing else.

One more question once I get this figured out.

I know electromechanical relays don't move quickly enough to provide PWM directly, so if I wanted to use the PWM enabled pins to fade the LEDs through the relay, would I somehow open each relay and THEN send the PWM signal through? Is this possible?

of the 3 wires on the relays.. One outside wire is the hot wire from the 12 volt. middle wire is usually used by the controller for the 5v input to trip it.. and the other outside wire is the hot wire to the lights.

the ground wire should go from the ground of the 12v source to the ground wire of the lights.

To the best of my understanding, you cannot use pwm with the relays... it's either on or off..

You could use MOS fets to turn on the LEDs and then use PWM directly.

Google is your friend

but I just can't wrap my head around how to wire this up.

What does that mean exactly ?
1- You are not familiar with led basics (ie: forward voltage drop, forward current, need for current limiting resistor etc....)
2- You don't know how to calculate the current limiting resistor.
3- You are not familiar with relay basics (ie: coil resistance, coil current, contact nomenclature (ie: COM, NO, NC)
4- All of the above
5- You haven't read or don't know how to interpret the datasheet for the leds
6- FYI, your schematic is wrong. The common of the relay contacts should be pivoting
from the left and select either of the two outside contacts, one is normally closed, and the other normally open. The Normally Open one NO is the one you want to use if want the led OFF when the relay is OFF. The NC is the one you want if you want the LED ON when the relay is OFF.