There are only two areas which require regular chassis greasing: the front suspension components and the steering linkage. These parts should be greased every 12 months or 7500 miles (12000 km) with an EP grease meeting GM specification 6031M.
If you choose to do this job yourself, you will need a hand operated grease gun, and a long flexible extension hose to reach the various grease fittings. You will also need a cartridge of the appropriate grease.
Press the hose fitting onto the grease fitting on the suspension or steering linkage component. Pump a few shots of grease into the fitting, until the rubber boot on the joint begins to expand, indicating that the joint is full. Remove the gun from the fitting. Be careful not to overfill the joints, which will rupture the rubber boots, allowing the entry of dirt. You can keep the grease fittings clean by covering them with a small square of tin foil or rubber caps which are available from aftermarket stores.