To get the faulted engine piston of your 1968 Buick Riviera fixed, one is required to remove the ridge covering each cylinder and turn the engine block upside down. You are also required to get rid of the connecting rod caps of the engine system. You can get more directions on how to do this from http://www.ehow.com/how_2321779_change-pistons.html though I would recommend you to use the advice of a skilled mechanic on this to avoid any complications.
Wait a minute. Something doesn't sound right here. You said one out of four is not working? I don't think there is any such thing as a 1968 Buick Riviera with a four cylinder engine. I think they all had V8 engines. Also I would check every other possibility first. It could be a bad plug or wire. Make sure they are getting spark to the cylinder. Robertayuk said to do a compression check. If you did that and one cylinder has low compression you can squirt some 30 weight oil in it if your compression comes up then you have bad rings if it doesn't then you probably have a blown head gasket or cracked head. Anyway Robertayuk knows what he's talking about and a compression check will tell you a lot. You can also have a leak down test done and this will tell you why your compression is low. It's easier to fix a blown head gasket than replace your engine if the rest of your engine is good. Even if you have to replace the engine if your Riv is in good shape it's probably worth it. Those are nice cars. I had a girlfriend with a 67 Riv. I don't know which made me sadder losing her or her car. I know which I'd rather have now. Anyway make sure you get an accurate diagnosis before forking over big bucks for major repairs and if you have a 68 Riviera I'm pretty sure that ain't a 4 banger. Good Luck with that classic!