Wiring dimmer in box were hot wires are joined
First off, good for you. You want to figure out what's hot and what's the load wires before disconnecting everything. With the power off, pull the switches out of the box and pull out the bare copper ground just a bit. If there's a group of white wires, neutrals, you can remove the wire nut but don't untwist the wires. Make sure none of the groups of wires are touching each other. Now you can turn the power back on. Take the common (usually black) probe from your multi meter and touch the group of white wires and take the + probe, usually red, and touch it to the black wires one at a time where they are screwed into the switches. With the switches off, when you get 120 Volts +-,  those are your hot or feed wires and those will be pigtailed to both switches if one breaker controls both switches. The other wires connected to the switches are the loads.
Once you determine the hot wires by doing the above, take your black probe and put it on the bare copper ground wire and the red probe on a black hot wire. You should get 120 Volts+-.
Now you know you've got a ground and if it's connected to the metal box, the box is grounded too.
Make sure your meter is set to &quot;AC Voltage&quot; and the proper range. Since it's AC and not DC, you'll get the same readings when you reverse the probes.
Turn the power back off and connect your dimmers according to the diagram, recap the white wires, and connect your switch ground wire to the ground from the dimmers and push the switches back into the box and screw them in. Turn the power back on and test everything.