how to cleanse a crystal(amethyst) pendant?

There are several ways to discharge negative energies form an object.

Moonlight, sunlight, salt, and water are all known for their cleansing properties.

So you could…
Leave it overnight where the moon will shine on it (through a window is ok.)

Let the noon sun shine on it (good for adding positive energies as well.)

Stir salt into water (stir clockwise) and then let the crystal sit in it overnight. Throw out the water the next morning.

Cleansing crystals differs depending on its type. Since you have amethyst, these are the 4 best things you can do:

1. You can give it a moon bath (leave it under the moonlight to recharge its energy

2. Water cleansing. Put your crystal under running water for a while, imagining that all the negative energies are being washed away

3. Avoid sunlight as the colours will fade
4. Do not submerge it in salt as salt will scratch the Crystal. You don’t like a scratched pendant, don’t you?

Soap.

Bury it in the earth through the waning moon phase (from the full moon until there is no moon) to absorb all negativity into the ground, then pass it through a fresh water stream to cleanse, sprinkle a circle of sea salt around it under the full moon, the salt cleanses and the moon dew regenerates it. Burn incense (frankincense) and bless it with your intention, saying at the end ‘for the highest good of all’. Set in on your window sill to absorb the suns rays. You have then cleansed it using each element.

I agree with Nini – choosing a cleansing method for a crystal depends on the type of crystal. I would avoid salt and sunlight with amethyst.

I tend to smudge my crystals to cleanse them (smudging with sage or some similar herb is a Native American practice) and I find it works fine, and I don’t risk damaging the crystal.

Here are some links that may help you:
http://www.millenniumminerals.com/resources/clean.html
http://healing.about.com/od/crystaltherapy/Crystal_Therapy.htm

http://www.crystalinks.com/smudging.html

Wash it, sit it in a window through an entire sunny day, and a night of a full moon.