On construction sites, you will often have to use a forklift designed to handle the terrain. Many forklift brands are designed so that they really work best in a warehouse or store environment - their engines are efficient, but don't have much heft, and their tires aren't really built to handle a situation where they might have to go off of a paved road. Rough terrain forklifts are the solution. Most companies make at least one brand that fits within this category. What you should look for:
1) A gas engine. Electric engines are great for saving you money and helping the environment and all that - but they don't cut it for getting over humps of dirt or pushing the forklift over uneven terrain. A rough terrain forklift should probably have a gas engine - giving it the power to get it over any obstacles or inclines. Another reason you need these is that in larger work areas such as construction yards or lumber yards, you need the greater speed they give you. Forklifts used solely indoors can go a little slower - they're working in cramped spaces anyway so they can't go at top speed. Outdoors, you are wasting time and money if you've got a slow engine.
2) Pneumatic tires - these are tires that help driving over uneven surfaces. They're a lot like the tires on your car - rubber and filled up with air. The tires usually used on forklifts won't deal well with rough terrain, and an all-terrain forklift will be better able to avoid punctures and other damage.
You can get used rough terrain forklifts online here: