Your car's underbody fights an ongoing battle against corrosion, though a few simple steps can help keep it rust-free.
Thoroughly flush road-salt residue with a garden hose. If you are using a public car wash, ensure they are not recirculating the water, which means you are washing & rinsing with some other car's salty run-off. Spray especially well inside wheel wells and on the underbody, where accumulated mud and leaves can trap moisture, creating ideal conditions for rust. Use a stiff brush to remove any clinging bits that your hose misses.
Check for any missing or loose splash guards or inner fender panels. These must be reattached or replaced to provide proper protection for your car.
Many vehicle doors have drain holes that can become plugged. This helps rain that gets into the door via the window assembly drain from the door. Use a thin wire or pipe cleaner to scrape them clear. Clogged drain holes can help corrosion rust from the inside out even quicker than even the car's exposed underside might. Similarly, inspect suspension components like the top of control arms for pockets of mud and road debris.
Once each month, get under your car and inspect for clogged drain holes, missing plugs, and loose undercoating. These all provide a place for salt and mud to collect and come in contact with the metal panels. Pry loose any corroded or cracked undercoating with a putty knife, then wire-brush and clean the area with solvent. Respray with spray-can undercoating, which you can buy at most auto parts stores.