Please keep in mind that Raze currently is in alpha stage, it is not version 1.0, as a result not all features planned for it are currently implemented.
Currently this only works for Duke Nukem 3D, I haven't tested the other games which I believe have no meaningful mod loading support as of yet. But here is how you do it for Duke. For those unfamiliar with it, most game logic in this game is defined through .CON files, of which there tend to be several of. In order to properly launch a Duke3d mod in Raze, you will need to find the main .CON file which in its parameters loads other .CON files alongside it. Here is an example from an old mod called God of War, the GRP of which has been taken from NightFright's excellent duke3d addon compilation:

As you can see,in this case, the file GODGAME.CON references GS-DEFS.CON and GS-USER.CON (which can be seen on the left side as being part of the same .grp - they are simply not loaded automatically), both of which have data that's necessary in order for the mod to function properly, but because it is GODGAME.CON that references these, it means that it is the primary .CON file and the one you should be loading. Whenever you want to know which the main .CON file is, you should always be on the lookout for the "include" parameters as seen in the screenshot above.
Now this is where it may appear counterintuitive for those familiar with the GZDoom way of loading mods. What you need to do is extract the primary .CON file and place it in the main Raze folder. Then, you're going to want to open the command prompt (or make a .BAT file or whatever method you prefer) and load mods in this way:

The -con parameter has to reference the primary .CON file as I explained above, whereas the -file parameter can take in any .GRP file or .DAT file or folder, so you have a wide variety of options to choose from in this sense. Here I successfully load Complex, an old levelpack, using its GRP, as well as Pray Your Prayers, a classic Duke3D mod with a number of new weapons, graphics and gameplay changes, using a folder. If you feel like trying this out for yourself, here is a link to Pray Your Prayers, simply unzip this into the Raze directory and used the command as posted above to get it to launch. It works flawlessly

When it comes to maps, the process is a bit simpler. Simply place the .MAP file you want to play in the Raze directory and launch it using the -map parameter and the filename, and Raze will directly boot into it.
Enjoy! Let me know if you have any questions.