Inspect your engine while it's running. Listen for any sucking or hissing sounds, which might indicate that an air hose or vacuum hose is loose or disconnected. If you find loose or disconnected hoses, reattach them and see if that solves your problem.
Listen to see if your engine is missing. An engine that is missing can cause a vibration because one or more of the cylinders are not firing. If you believe that you detect a miss from the engine, pull out a few spark plugs and look at their condition. If they are very dirty and worn, change them and see if this stops your engine from missing.
Inspect your ignition wires. See if they are cracked from the heat of the engine. Make sure that they are tightly connected to the spark plugs and to the distributor. A good way to see if they are defective is to put the car in gear, and while your foot is mashing the brake, rev the car and see if it starts missing. This is a good way to put a "load" on the engine to see if the wires hold up.
Check from underneath the engine and look at your engine mounts. These are the thick rubber blocks that are between the chassis and the engine. Sometimes they are filled with hydraulic liquid. If so, make sure it isn't leaking. Check your mounts by inserting a crowbar between the engine and the chassis. Put pressure on it, moving the engine away from the chassis. If you see that the motor mounts are cracked or damaged, you may want to take your vehicle to an automotive technician to have your motor mounts replaced.
Check your harmonic balancer. Harmonic vibrations can lead to a variety of mechanical failures. Harmonic vibrations are specific and usually have a repeated type of vibration which ebbs and rises. One indication of your harmonic balancer being worn is if you detect a leak from your front main seal. If the above steps don't fix your problem, take your car to a professional and have them check the harmonic balancer.