Step 1: Join PostCrossings
This is free, but you will need an email account (not unlike this fine site).
As a personal note, I suggest you mention your hobbies and the kinds of cards you would like to receive on your profile. This helps people sending you a card to select a card that best fits you interests. I also suggest a face picture, but understand that some people feel uncomfortable with that.
Step 2: Buy or Make Some Postcards
You can be creative and follow some of the instructables on this fine site to create your own post cards. Be sure to stay to the standard size (4" x 6" in the US) to improve the chances of your card being delivered successfully around the world.
On the other hand, you can go to the "drug store" (Walgreens in my area) and buy some post cards featuring local monuments or locations (like the post card of the Gateway Arch shown here). You can also choose funny or sexy postcards (as one of the people I sent a card requested) since the cards in your country are likely to be quite different from cards in other countries.
Step 3: Request an Address (up to 5)
When you get an address you will also get a postcard ID that you need to place on the card. When the recipient gets the card they need to enter that code into the website to mark the card as received. When that happens you will be allowed to request a new address and you will be put in the queue to receive a card.
Step 4: Fill Out the Postcard and Mail It
1) The stamp goes in the upper right corner. I put this on first so that I don't cover up any text I put on the card.
2) Do not write in the bottom 1/2 inch or so (see picture) since the automated sorting bar code goes there. You can see on the card I received how the ID was printed over.
3) The address of the recipient goes on the right side under the stamp and above the clear area at the bottom of the card. I don't suggest putting the PostCard ID here in case it gets confused with the address.
4) On the left side write the post card ID clearly so that the recipient can easily read it. If they can not read and enter the ID, you will never get "credit" for the card and it will be considered to be in the mail.
5) Last but not least, write a nice note to the person, perhaps explaining the significance of the picture on the card if the card does not (this example does).
Now go stick it in the mail and check the PostCrossings web site to see if it has been received.
Finally, a quick note about language. The web site assumes that all cards are in English (or one of its derivatives like American). Some people will say in their profile that they accept cards in other languages, but unless they do, stick to English.
Step 5: Get a Card in the Mail!
Finally after much waiting, you will get an email that one of your cards has been registered. On the web site you can see how long it took to get there and you might even get a nice note from the recipient. Also, now you can send another card since one has been marked as received.
And then ...
The day will come when you get a postcard from some place in the world far from your home. My first card was from Finland and I live in the US. I have never been to Finland, but now I feel more connected to the country some how.
Hopefully this will get you interested in a new (and very cheap) hobby that just might bring the world a little closer together.