Remove all necessary suspension parts so you can gain easy access to the existing bushing that you need to remove. The exact process will differ greatly and it helps to have a repair manual for your application. For example, if you are replacing the bushings on your John Deere lawn tractor, you can obtain a service manual that tells you how to take the front suspension apart. In most cases, you will need a socket set to remove the components.
Pry the old bushing out of the bushing cup with a flathead screwdriver or with a pair of pliers. You will likely damage the bushing by taking it out, but this is okay -- you will not reuse the old bushing.
Clean all of the dirt, debris and grease out of the bushing cup with a rag. Most OEM bushings have a grease fitting attached to the cup that allows you to service the bushing with a little grease.
Press the urethane bushing into the bushing cup. The urethane bushing will be a tight fit and will likely start to push itself out of the cup. This is normal. Hold the bushing in with your fingers.
Reassemble the components and then slide the bolt through the components and the bushing. For example, if you are replacing a lower-control arm on your Lawn mower -- after you press both control arm bushings into the cups on the control arm -- place the control arm onto the suspension and then slide the bolt through the control arm. This will hold everything in place.
Tighten the bolts with a wrench to lock the control arm in place.