Urban exploration involves the investigation of manmade structures not designed for public consumption, any place that you're not supposed to go. Abandoned buildings, utility tunnels, construction sites, bridges, roof tops, service areas, train or bus yards, basements, boats, churches, drains, catacombs, hotels, hospitals, transit tunnels, mechanical rooms, etc.
These things may be helpful when exploring: flashlight (a must!), a small med. kit, water, some small tools, moist towelettes, camera, dust mask, a backpack.
Dress appropriately. Dark colors, sensible shoes. I prefer light gray, the color of shadows.
Sometimes I'll dress as a security guard.
Before entering, you should make sure you are not being observed. listen. Once convinced that the coast is clear, you may enter. Explore abandoned sites slowly and never go alone.
While in a building, be sure to have more then one escape route. This also applies to steam tunnels, construction sites, any place you're exploring.
If you hear any strange sounds, you should be quiet and hide, or escape like a bat out of hell. If you're caught in an area for authorized personnel only, tell them that you thought that you were authorized.
It's important to use a flashlight. You don't want to fall down a shaft or hit your head on a cement pillar.
Equally important is to cup the light in your hands, letting small amounts though your fingers, and aim it to the floor, away from windows. Shining a light in an area that's supposedly unoccupied is like sending up a flare.
If you come across chemical/radiation/bio-hazards you should limit your exposure. Safety first.
Old elevators are dangerous and should be avoided. You don't want to wake up dead after falling down a shaft.
In an abandoned building, stairs are your main option for vertical movement. Stairs and ladders also lead to places not accessible by elevators.
Feel free to use force to gain entrance into an abandoned building. Never vandalize, steal or damage anything, don't even litter. Don't harm the places you explore.
Try to leave no trace. If others have burned (i.e.: vandalized) the location then it may be acceptable to perform a salvage operation. Recycle what thou wilt.
Always know the way out. Try not to be observed leaving.