There are four things you will need:
Wax: be sure to buy ski or snowboard wax that is designed to be applied with a hot iron. There are plenty of choices, but a good all-temperature wax will work well in most snow conditions. Keep in mind that if you are going to be riding in temperatures above 32 degrees (spring skiing for example), a warmer weather wax would be preferable. The same applies to cold weather, for temperatures below 18 degrees or so you should select a cold weather wax. We suggest you experiment with different brands and varieties of wax, find what works best for you.
Scraper: pick this up at your favorite board shop along with the wax. Plastic or metal scrapers are both fine, just avoid really wide scrapers that are sometimes marketed for snowboards - they don't scrape as well as the smaller ones.
Iron: now might be a good time to invest in an iron designed especially for waxing skis and snowboards. These are smooth on the bottom and therefore apply a nice smooth coat of wax. Or you can go down to your nearest Salvation Army or Goodwill and pick up a used household iron for a few bucks.
Scotchbrite/SOS pads: these rough green pads are available at any grocery store next to the kitchen sponges.
Some optional but helpful items:
Base Cleaner: if your snowboard's base is dirty, clean it using a base cleaner (find this at your board shop) and a rag before you hot wax it.
Vices: setting up a workbench makes tuning and waxing your board much easier. Vices are available that hold your snowboard in place while you work.
There are essentially 4 steps; drip, iron, scrape, buff. Lets get started:
Drip
Put down an old sheet or some newspaper to catch dripping wax. Then put your board/skis base-up on your new vices (see optional items) or on some books.
Plug in your iron and set it to a medium heat. It should be hot enough to readily melt the wax, but not so hot that the wax smokes (important!). Hold the iron perpendicular to your board/skis with the pointed side down. Press the wax bar against the hot iron and hold it there. As the wax drips, move the iron up and down the along the base until you have stripes of dripped wax 1 to 2 inches apart. The wax will spread out a lot once you iron it in. Excess wax will be scraped off, but take care not to waste it. Set the wax aside.
Iron
Now iron in all that wax until the base of your board is fully covered. Keep the iron moving; leaving it in one area for too long can damage the snowboard.
Scrape
Turn off the iron and wait 15 to 20 minutes for the wax to set and cool. Now grab the scraper and scrape off any excess wax in a nose to tail motion. Scraping away all the wax may sound counter-productive, until you realize that a hot wax actually opens up the pores in a snowboard's base where you want wax to go. Excess wax will only slow you down.
Buff
After scraping, rub the scotchbrite pad in a nose to tail motion to take off the last of the wax and give your board a finishing touch. Don't worry about getting to technical with this step, just rough up the freshly waxed base a bit, until it gets that nice rough wax look. You are now ready to ride, have fun out there!