Virtually all countries require work permits or visas before you can work there legally. Most will only allow foreign workers to fill positions if there are no locals who are qualified. Some countries even require an employer to release wanted ads in newspapers for a particular position for a specified time period. If no qualified local responds to the ad, then a foreigner can be hired for the position.
Different countries have a different set of requirements and standards for those who wish to obtain work permits. One of the best ways to find out how you can obtain a working visa is to ask expats or prospective employers.
The following site will link you to some pages that will provide some information on travel requirements and obtaining work permits:
Foreign Consular Offices and Embassies in the U.S.
This is a complete listing of foreign consulates and embassies throughout the United States. It is useful and usually necessary to contact them to inquire about visa requirements before planning any overseas trip.
Remember that trying to find an overseas job is much like looking for any other job. You must be able to sell yourself. A first impression, or good packaging, will do you wonders, but it is far more important to have quality within that package than anything else.
Finding decent-paying computer work overseas, especially after arrival, is feasible but difficult. I recommend telecommuting with a company in your home country. It is easier to find work, the pay is better, and you can take advantage of good dollar exchange rates and low costs of living.