Distilled water. Make sure the water is clean and free of minerals. To be safe, don't use tap water, especially if your water is either hard groundwater or city water which is often fluoridated, chlorinated or otherwise treated. Rainwater won't cut it either, as there tends to be a lot of dust particulates caught in the droplets as they fall towards the earth. Bottled water is your best best, though make sure that it doesn't have any additional additives such as for flavor or nutrition. These things might not just stain your LCD screen, but potentially even scratch and permanently damage it.
Note, the water does not necessarily need to be deionized. While this is another way to guarantee purity of water, and arguably a more effective one at that, it is more difficult to come across and there is no real improvement in its use as a cleaning solution.
Isopropyl Alcohol. This can be purchased for cheap at virtually any supermarket or electronics store, more commonly under the name of “rubbing alcohol." Chances are, you probably already have some in your house! Make sure that it has not been mixed with anything, or already unduly diluted with water.
While this may seem obvious to some, particularly those who have read the label, isopropyl alcohol is highly toxic. Not toxic in the sense of ethanol, the sort of alcohol in wine and beer that will fry your liver in high quantities—really toxic.
Now, in a pinch, you can use straight water, albeit as pure as you can get it, and if you have it, unflavored drinking alcohols just as plain Absolut Vodka. However, while they clean you LCD screen well in the short run, they are not a cleaning solution you should engage with on a regular basis, as repeated use may shorten the lifespan of your LCD screen.
Plastic bowl and spoon. Really, these may be made out of any material, as long as the isopropyl alcohol won't soak into it like with wood.