Leviton three way has two red, one black plus ground. Old switch one each,white,black red. What goes where.

SOURCE: Trimatron 3 way push on off dimmer switch

One wire is the common and the other two are the travelers.The trick is to find which one is which.... If you can see into the electrical box check to see if one of the red wires and the black wire are from the same cable, if they are then more than likely those two wires are the travelers; you can also look at the other switch and see which two wires are on the brass colored screws, those would also be travelers. The common is usually the wire that is on the black colored screw. Once you figure out which wire is your common, I'm thinking that it is one of your red wires, you would attach that wire to the black wire on the dimmer and the other two wires to the 2 red wires on your dimmer.

SOURCE: Have a Leviton dimmer with red, black and green

You are correct in assuming green is the ground and connects to bare copper wire. Black is always the HOT wire and should be attached to the black wire. Red wire connects to white wire.

SOURCE: i have a black wire a white wire and a ground

The red wire is your chase wire and needs to go all the way to the other switch

SOURCE: I have tried to install the Single Pole Leviton #

Sounds like that dimmer you ruined
You must turn off power when replacing
And test the wires

SOURCE: I would like to install

The circuit you are working on is a 3-location circuit - where two of the devices were 3-way switches, and the remaining device (the one you are trying to replace with a dimmer) is a 4-way switch. Standard dimmers like the one you're using CAN NOT be used to replace a 4-way location. If you wanted to use it to replace either of the 3-way switches, that's no problem - but what you're doing right now will not work.

If you absolutely want to dim the lights from that specific electrical box, my suggestion is to upgrade to a "smart dimmer" where instead of a basic dimmer and two light switches, you have three devices that talk to one another and all dim the lights together.

In terms of your ground wire questions - ground wires certainly aren't necessary to make the whole thing work - rather they're there for safety. Sometimes installers will ground the device by connecting the ground wire to the backbox (assuming its metal) and then rely on the mounting screws on the dimmer or switch to perform the grounding. There are some code rules/exceptions for allowing the device to not be grounded (usually when its in a plastic, non-combustible backbox). If you want to make sure everything is completely up to code (which are usually goverened by local municipalities), you should consult a licensed electrician - but above all else, just use good judgement. Long story short, if the devices weren't grounded before, you can't make it any worse.