Step 1: Real hardware... or emulation?
First of all, if you've got your hands on real original 80's or 90's Macintosh hardware and want to try on it, then you diserve a handful of internets my friend! That's awesome! The challenge you will face is how to input files you get from the internet into the old Mac. To do this, you will need a floppy drive and MacDisk (or Basilisk II) to help you copy files on a floppy disk that you will insert into the old Mac.
Out of luck for a real Mac and only got emulation to try? It's OK, that's how most people do nowadays anyway. Here is the best selection of emulators that will allow you to run every single classic Mac OS version ever released:
SheepShaver, a PowerPC emulator runs Mac OS 9.0.4 down to Mac OS 7.5.2
└─── BEST FOR: 1995 to 2001-ish PPC software
Basilisk II, a color 68K emulator, runs Mac OS 8.1 down to Mac OS 7.0 (can read/write on 1.4MB floppy disks!)
└─── BEST FOR: 90's 68K software and making backups of your old floppy disks before it's too late!
Mini vMac, a B&W Mac Plus (68k) emulator, runs Mac OS 7.5.5 down to the original Mac OS 1.0 from 1984
└─── BEST FOR: 80's B&W software that typically runs on a 9 inch screen
QEMU with PPC OpenBIOS, an emulator capable of running Mac OS 9.1, 9.2 and early Mac OS X (10.0 to 10.5)
└─── EXPERIMENTAL / summer 2016: no sound, very slow, but boots Mac OS 9.2.2 and early Mac OS X versions
So, depending on which version of Mac OS (and/or CPU) you'd like to emulate, you need to choose the above emulator accordingly.
Step 2: Basic System Tools
STUFFIT EXPANDER... What most people get confused with is how old Macintosh files were stored. Unlike any other platform (Windows, Mac OS X, etc...) the files on earlier Mac OS versions contained a resource fork that *COULD NOT* be transfered/stored on anything else but a Macintosh file system, except when compressed with Stuffit or BinHex. That's why every file you see on the internet for download to an old Mac OS ends with .sit or .hqx. To uncompress those "stuffed" archive files, if you run Mac OS 7.5 or newer, you need Stuffit Expander 5.5. For anything earlier than Mac OS 7.5 you can grab a copy of Stuffit Expander 3.5.1 but note that it does not extract some of the archives made with Stuffit 4.x or newer. The file compression standard in the 80's was Mac Binary anyway, which Stuffit Expander can extract among other formats. Stuffit Expander needs to be on your system before attempting to copy files from any source, so here's Catch-22: When you set up an old Mac OS that does not come with Stuffit Expander, how can you transfer Stuffit Expander itself from a PC computer without destroying its resource fork since you can't uncompress Stuffit Expander without Stuffit Expander, right? That's the only situation where you need to use the Basilisk II emulator, which has integrated floppy drive support, so you can uncompress Stuffit Expander and copy it, complete with its resource fork onto the floppy disk, which should open fine on the old Mac computer afterwards and allow you to transfer compressed files from now on using traditional ways. Any .sit or .hqx file can be transfered on any file system, Mac formatted or not, without getting corrupted.
DISKCOPY... You will find other types of archives that we call disk images (files ending with .img). DiskCopy is Apple's tool that shipped with classic Mac OS version 6.x up to Mac OS 9.2.2 that allowed for a perfect replication of a disk or a folder with everything in it, keeping the window and icon layout/positions, comments, color labels you might have applied, creation/modification dates, etc... it looks good, except that as previously stated, since they're not .sit or .hqx files, they *CANNOT* be moved/stored on a non-Macintosh file system, since this would render the disk image corrupted. Always Stuff (.sit) or BinHex (.hqx) all your files before moving/storing them outside of the classic Mac OS, disk images created with DiskCopy included. There is a way to make classic Mac OS disk images binary safe (for example if the image is created with special software in Windows or Linux, resulting in a slightly different format, like .dsk file instead of .img) but the ones created by DiskCopy are not.
TOAST... it creates (backup), mounts and even burns CD-ROM disk images like .iso and .bin. It can also copy CD-ROM's to CD-R directly. You will need Toast if you plan on downloading CD-ROM .iso disk images or if you want to backup/archive your own CD-ROM's before it's too late. If you're using Mac OS 7.x you can grab a copy of Toast Deluxe 4 and if you're running 8.5 or 9.x then get a copy of Toast 5 Titanium instead.
MACDISK (for Windows)... if you want to move files from a PC to an old Mac OS (or the opposite) using floppy disks, then you will need a tool called MacDisk. This program allows Windows OS to format, read and write files on Macintosh formated floppy disks (also supports CD-ROM, USB drives, Iomega ZIP drives, etc...) but *NOT* on the older 800KB or 400KB floppies, it only works with regular 1.4MB floppy disks. Keep in mind while using this program that if you copy old Mac files on a PC file system, it will instantly lose the resource fork and this will permanently corrupt them, unless you compressed them as .sit or .hqx under Mac OS beforehand. MacDisk is useful in the scenario where you already compressed (.sit) your files and you want them copied onto a Macintosh formated disk. Once you insert the disk on the old Mac, then using Stuffit Expander you will be able to extract and use the files. Note that if you use Basilisk II as an emulator, it already has integrated Mac floppy disk support, effectively using your PC floppy drive so you do not need MacDisk, you could just insert your floppy disk in the drive and Basilisk II will mount it in the Mac OS so you can directly use it.
Looking for a "fast" (10/100/1000 mbps) PCI network card for your old PowerMac that works on both Mac OS 9 and Mac OS X ? D-Link DGE-528T is one of the rare universally compatible fast PCI network cards reported to work both on Mac OS 9.2 and Mac OS X 10.2.
Transfering files between 2 old Macs via serial connection
Using AppleTalk, very old Macs could be hooked up together via the printer port. Read the instructions on this Classic Mac sharing guide.