First you need to generate a key pair. (Actually, it's four numbers: p, q, d, and e: p * q and e make the "public key" and p, q, and d make the "private key.") This is the slowest part. Pick how large a key you want. Larger keys are more secure, but take longer to generate, and somewhat longer to use (especially decrypting the orders). 512 bit key modulos (32 byte keys, ie p and q are 256 bits each) are still considered somewhat secure. My browser took about 3 minutes to generate a key of this size on my p2-450. Try a smaller one first, like 8 bytes and square that time twice to see how long it might take for you.
Encrypting the orders takes very little time, maybe a second or two, but those decrypting will notice a definate lag (7 seconds for me).
Note that many browsers require you to NOT cancel the script after it is taking a while to generate the keys. I've tested this on InternetExplorer 5 (win). If you find it works/doesn't work with another browser, let me know. I've been told that Netscape is much slower than Microsoft for this type of thing.
Zed's Mods to this: So, I'm using persist.js to store the key you initially generate into the available private store in your brower. Browsers have some forms of storage other than cookies, and persist.js makes this possible to use on most of them. What you do is put in a chunk of randomness from random.org and hit the GenerateKey button. Now you've got yourself a private/public key combo stored to your browser. Alright, close this window and come back and the browser will remember it, without any intervention from any software on my server. What's that good for? Just wait and see my friend.
To make a new key, simply kit the RemoveKey button, make sure some randomness is in the randomness box, and hit GenerateKey again. You'll get a new one and it'll be stored for you again. Try out an encryption, copy the encrypted text, close the browser, come back and you'll be able to decrypt it.