How easily does the engine start? How smoothly does it idle? Is the vibration regular or irregular, and does it go with engine speed?
Are there any accompanying noises?
If the vibration's regular, goes with engine speed, and there are accompanying noises, remove all the spark plugs and turn the engine over by hand. (Put the fan belt back on for this.) With the plugs out, the engine should turn over smoothly, with some but not too much effort. And the effort should be constant. If the motor feels like it binds in any position, or if there are clunking sounds as you turn the engine over, that's cause for concern, and needs to be investigated further.
If the vibration is regular, goes with engine speed, but the motor's quiet, put the spark plugs back in and turn the engine over by hand. You'll be fighting against engine compression this time. As each cylinder goes into its compression stroke, you should feel quite a bit of resistance, and a muffled "sssh" sound deep in the engine's guts. This is the sound of compressed air leaking past the piston rings, and is normal. All six cylinders should put up the same amount of fight, and you should hear the same "ssh"
sound with all six. You have to turn the motor over at least two revolutions to do this. If the engine puts up noticeably less resistance on some compression strokes than on others, that indicates bad compressions, and you might even have to get out with a compression tester to confirm it. Bad compressions mean either head gasket troubles, valve troubles (both of these are a head-off job), or worn or broken rings.
It's a good idea to give the ignition system a quick test. Start the engine and let it idle. If the car has its original plug leads, short each plug to ground with a screwdriver: put the shaft of the screwdriver against the rocker cover and slide the screwdriver down until the tip touches the spark plug terminal. This way you won't get zapped
If your ignition leads have boots on them, unplug the leads from the plugs, one at a time, and put them back. Note how the engine note changes as you disable each cylinder in turn. A healthy engine will go "chuff-chuff-chuff" when you pull a lead. If your engine is running on five cylinders, the engine note will not change when you pull the ignition lead from the bad cylinder.
In this case, listen to the sound of the spark as you begin to pull the lead off the plug. If the ignition system's good, you'll hear a sharp "tick-tick-tick" sound as you begin to remove the lead. This is the sound of the spark.
If the spark is bad at any cylinder, you need to investigate your ignition system.
If the spark is good at all cylinders, but the engine runs badly, then you have fuel system troubles, or bad compressions.
If the vibration is irregular, and only really happens when you speed the engine up, it may be something as simple as over-advanced ignition timing. Disconnect the vacuum advance pipe from the front of the distributor, start the engine and see whether there's any improvement. If things get better, you need to retard your ignition timing.
Sorry: this post has been both too brief and too long.
Rob