I'm not sure where else to ask this but here goes. So I recently picked up a game and have been trying to mount my DVD drive in DOSBox but I have no real idea how to parse it. I know how to go about it in Windows, but not Linux.
Any help would be appreciated.

Firstly, welcome!
Secondly… how do I put it… DVD and DOS (most probably MSDOS) do not usually mix together.

Anyway. when it comes to games maybe the most efficient way of doing things is to unpack all the DVD contents (honestly, a DOS game on DVD? Come on!) into some directory and then to follow the usual DOSBox procedure of mounting that directory as a drive inside DOSBox.

The mounting procedure itself is no different than on Windows®. After all, it is still the same DOSBox.

Granted, some (Windows®) games actually check for the presence of the authentic physical CD. But in this case I believe it won't work on Windows® either. Besides, I assume it is a DOS game we are talking about (what game, btw?), hence, not our case.

Or you can mount (in the DOSBox) the drive contents directly, after accessing them in the file browser (usually discs are being auto-mounted in the "/run/media/<username>/<discname>" directory, but that can depend on the distro), yet, I do not recommend it as the mounting is per-session and you will have to redo it everytime (or to construct an elaborate launching shell script).

Okay, so I ripped the game into it's own directory where i keep my regular DOSGames (USNFINSTALL), and attempted to run the install but was hit with a "CD must be available in the drive" prompt. Would it be easier to make and mount an ISO instead?
And if so, is the mounting process similar to mounting a directory?

quick edit:
oh and btw the game is US Navy Fighters.

This should do it. :) As was said by previous poster, the "-t cdrom" part should hopefully fool the installer into thinking it deals with CD-ROM and not HDD.

You can even mount the already unpacked disc contents this way (no need to insert the disc itself anymore).

Just be warned (albeit, you probably know this already): some installers of that era actually have some sort of protection and will refuse to recognize a CD-ROM if its letter is "C:", so you should probably mount another directory as your dedicated "C:" HDD and the unpacked installer as "E:" CDROM. :)

using an ISO has the benefit that it also works for mixed mode CDs (ie CDs with audio & data tracks).
short version:

$ cdrdao read-cd --datafile image.bin --driver generic-mmc:0x20000 --device /dev/cdrom --read-raw image.toc
$ toc2cue image.toc image.cue

then inside DOSBOX use imgmount instead of mount:
imgmount d "/tmp/image.cue" -t iso -fs iso

more info here
https://www.dosbox.com/wiki/IMGMOUNT
https://www.dosbox.com/wiki/Cuesheet

note that when you use the method outlined in the previous posts you might need to set the CD label in order for the game to accept the cdrom, ie.:
mount d "/run/media/<username>/<disclabel>" -t cdrom -label <disclabel>