Dumping games is done on a console by console basis - it all depends on what you want to dump. Disc-based console games, in general, are easier to rip as you can, for many of them, simply insert the disc into your computer's disc drive and create an iso image (for example for Saturn, PS1, PS2 games). For Dreamcast games, since they're GD-ROMs, you either need a modified disc drive or a way to connect your Dreamcast to your PC (for example with a coders cable, though that method is very slow) and use the Dreamcast as a GD-ROM drive. PSP games are dumped by using custom firmware on the PSP, setting the USB device to the UMD drive and then simply copying the file from the PSP to your computer via USB. GameCube and Wii games are best ripped from a Wii - using homebrew, you can dump inserted discs onto an SD card.
For cartridge based consoles, it's slightly more complicated. A good method for older cartridge games is Retrode and it's various hardware addons, iirc, but that's out of print by now and might be hard to get. For other cartridge systems, you'll need to look up individual solutions, like cartridge adapters. I don't know the details there though as I haven't yet fiddled with cartridge dumping, which is too expensive for me considering the usage I would get out of it.
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