Crossing the border is simple. Follow the signs at the immigration checkpoint and present your passport to get stamped out of Thailand. Don't forget to fill out the Thai departure card which is stapled inside your passport.
Then walk across the bridge that crosses the River Sai and pass through the entrance with the sign "The Republic of the Union of Myanmar" - the official name for Burma.
Again following the signs, present your passport to the Myanmar Immigration officers, who will charge 500 baht for an entry permit valid for 14 days. The option to pay $10 in US currency is no longer available (not surprising as $10 is worth only 300 baht these days). The Myanmar immigration officer then issues a pass but hangs on to your passport until your return. Leave the immigration office and you're in the Burmese town of Tachileik.
Whether you stay for 1 day or 14, you can't visit any other part of Burma - only Tachileik. To visit other parts of Burma requires a visa and a flight to Rangoon from Bangkok or Chiang Mai.
Thai people aren't required to pay the 500 baht but must first get a form from the 'ampur' (district office) by presenting their ID card and paying 30 baht. (Thai Passports aren't used at this border control). The office is situated 2 km from the border control on the same road (just off the road, in fact). The procedure only takes a couple of minutes. You can get there by motorcycle taxi near the border control for 20 baht. The driver will wait and take you back to the border control if you like.