You can use a plain RCA cable to connect a IIgs to a TV or monitor that supports composite input. (Meaning of course you might have to hijack the family TV.) Composite is far from ideal if you want to use the IIgs for anything besides games, but it should be enough to verify that the system works. Keep in mind it's not going to be very useful without a disk drive.
These days it is... nontrivial, to find new RGB monitors that will work directly with the IIgs. Here's an Apple knowledge base article with the pinout. The sync rate is half that of a standard VGA monitor (IE, the same as US NTSC) and most modern (IE, later than early 90's) "Multisync" units will refuse to work with less-than-VGA signals. Essentially the same monitors that work with the original Commodore Amiga (sans scan doubler) will work, which isn't a huge sample. If you don't want to find an original vintage monitor, well... there are adapters that can convert RGB to the Y-Pb-Pr Component video standard used by modern TVs, but you'll pay through the nose for that. Other options include looking for a TV with RGB input (some currently shipping High-Def TVs have analog RGB/VGA ports but I don't know if any of them will accept the IIgs's output), using a European TV with an RGB SCART connector, or finding/building a scan doubler with RGB input so you can use a VGA monitor. (This would probably work. There are also homebrew designs floating around although building one might not be much cheaper.)
These days it is... nontrivial, to find new RGB monitors that will work directly with the IIgs. Here's an Apple knowledge base article with the pinout. The sync rate is half that of a standard VGA monitor (IE, the same as US NTSC) and most modern (IE, later than early 90's) "Multisync" units will refuse to work with less-than-VGA signals. Essentially the same monitors that work with the original Commodore Amiga (sans scan doubler) will work, which isn't a huge sample. If you don't want to find an original vintage monitor, well... there are adapters that can convert RGB to the Y-Pb-Pr Component video standard used by modern TVs, but you'll pay through the nose for that. Other options include looking for a TV with RGB input (some currently shipping High-Def TVs have analog RGB/VGA ports but I don't know if any of them will accept the IIgs's output), using a European TV with an RGB SCART connector, or finding/building a scan doubler with RGB input so you can use a VGA monitor. (This would probably work. There are also homebrew designs floating around although building one might not be much cheaper.)