Clear out a trench along the natural pathway of the water. If you are installing a culvert under an existing driveway, you will need to remove that part of the driveway to get the culvert in.
Lay a 6-inch thick bed of gravel underneath the planned location of the culvert. Tamp the gravel down with the bucket of a backhoe or a construction vibrator.
Lay the culvert in place. A corrugated steel culvert is durable and will resist both the weight of passing vehicles and the impact of water and weather.
Backfill over the culvert with gravel. Keep the fill several feet away from the ends of the culvert to avoid dropping gravel where it will impede water flow. Alternatively, construct retaining walls of rock or brick above the ends of the culvert and backfill up to the retaining walls.
Replace the material of your driveway on top of the area that you backfilled. If your driveway is gravel or crushed stone, this is simply a matter of dumping a load of those materials and raking them over the area. A tarmac driveway will need a paving crew to pave over the affected area.
Landscape the areas on both ends of the culvert to help water flow naturally into its opening and away from its exit. Maintain a constant downhill direction to avoid pooling.