How to Earth (ground electrically) my laptop

There are two possibilities here.

One is that you are building up a static charge when walking across your carpet, sliding off of or onto your chair... something like that. When you touch metal on the laptop you are discharging that static charge. Does it happen more than once? If not, it's this sort of issue. The laptop is already providing a ground, so adding a grounding wire won't help.

What should help is grounding yourself to something else, preferably something with a high-resistance path to ground, before touching the laptop. Discharging through the resistance will cause it to happen gradually, so you won't feel the spark. One megohm or so is a good choice (this is typically what's in the anti-static grounding straps). If you don't know what that means, get a friend with good electronics construction knowledge to help you.

The other possibility is that the AC adapter of the laptop is "leaking" AC onto the laptop's chassis. If you feel it every time you touch whatever it is that you're touching, it is this sort of problem. This is an extremely dangerous situation, and it will not get better on its own. The cure is to replace the AC adapter... Preferably before you ever use the laptop again.

Jamie Hanrahan gave an excellent answer but I think there is another possibility apart from what he described. It seems that many people have zapping issues with their laptops and the zaps seem to be more than just static. See this page for a lot of examples

From that same page, a user responded with the following (and I quote):

"If you have the laptop in your lap, and if you are wearing shorts, the areas of your legs that are in contact with the screws will feel uncomfortably tingly - like there are pins being poked into the surface of your skin, but not deeply. The sweatier you are, the more galvanic reaction (the more it hurts). This is NOT a power supply problem, so getting another DC power supply is not going to cure the matter.

What this is, is the AC voltage that is sinked to ground through a number of circuits that rely on higher voltages stepped up through DC to DC converters (see: http://en.wikipedia.org/wiki/DC-to-DC_converter). Displays take higher voltages to operate. An oscillator converts the laptop's DC voltage to AC, steps up the voltage, rectifies it, then filters it. This is the residual AC voltage from that process. It is a byproduct of miniaturization and not having enough space for adequate shielding or having an adequate groundplane. You become part of the ground and might be a better ground than the rest of the device.

As the OP stated, 48 mA is usually not enough to disrupt your heart's electrical activity, but it is a big discomfort. At first, I used a book under the laptop. Then I took some black electrical tape and put it over each of the screws on the bottom of my Dell. It works, but then, the laptop also gets hot. That's another issue."

Connecting a crocodile clip between my network cable and a ground did fix the problem...HOWEVER AS MENTIONED BY OTHERS, YOU SHOULD NEVER MESS WITH ELECTRICITY WITHOUT PROFESSIONAL HELP. For example, if the AC adapter is leaking AC (as suggested by Jamie) and you touch the crocodile clip, YOU COULD BE ELECTROCUTED.

Here is a page describing similar ways to ground your laptop. AGAIN, ALTHOUGH IT MAY APPEAR SAFE, IT CAN BE VERY DANGEROUS TO EXPERIMENT WITH THESE DESCRIBED METHODS WITHOUT PROFESSIONAL HELP.