When I start my car, it vibrates in park and reverse. When I put it into drive, the vibration stops. If I let the car run for a while, the car will start vibrating even in drive.
On the Honda Civics the passenger side motor mounts are known to fail and can cause the issues of vibration that you are experiencing. These mounts are fluid filled, and often when they fail, you will notice a small amount of fluid leaking from the mount. Replacing the mount will require a way to suspend the engine safely. You may want to enlist the help of a mechanic, such as one from YourMechanic, who will have the proper tools and equipment to safely replace the mount without damaging the engine.
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