Short of going to a first-tier University AND having a campus job that allowed you near the ethernet jacks, you were either going to spend weeks downloading disk images over your 38.4 kbps modem, or you were going to buy a collection of Linux distributions + the Sunsite archive on a 5-cd set that was released quarterly and available at computer stores.
Assuming that your CDROM spoke standard ATAPI instead of some weird hooks-up-to-a-soundcard interface from 1994, you probably had to create a floppy boot disk by dd'ing it off the cdrom, as your BIOS was 50/50 able to support the El Torito extensions that allowed a CDROM to boot the computer.
The dialog-based installer wasn't too different from now, IIRC. I think it was Debian that had options for installing from not just floppy and ftp, but NFS as well.
Once the machine was booted, you hoped to see "LILO" was successfully installed to bootsector and you could choose which OS to boot. If LILO didn't install right, it would just present "LI" and a blinking cursor. If you still had DOS on the machine, the recourse was to use a DOS floppy boot disk and use the undocumented "fdisk /mbr" command to put a normal DOS boot sector back on your hard drive.
Once the machine was up, you most likely had to get PPP working with your modem. Hopefully you had an external modem. Minicom was close enough to Telix that you'd use that to make sure that AT commands were making it to the modem, and then you went down the rabbit hole from there.
Getting X working sucked. I think by 1998 there was a helper script for generating your XFree86 conf, but even that would most likely require some hand-tweaks. If at this point you had your modem working you could at least get online with PPP or even just a plain shell account to start searching DejaNews for hints on how to get that working.
dselect was awesome, it felt like being connected to the world's hugest BBS, where you were guaranteed that every piece of software in the archive would work on your machine.
Now you're a few days in: You've got X working (probably at a wonky refresh rate), you can connect to the Internet (when your ISP has an open line and you aren't hitting a busy signal) and you've got Netscape installed. Getting your soundcard working is probably still a week off.