To start messing around with fonts choose the menu item Format ▸ Font ▸ Show Fonts.
The Fonts Palette packs a lot of punch for being so small. This little window controls everything you could want to do with fonts. If you get confused about which button does what, hold your mouse over it for a second and a tool tip will be displayed.
There are Collections of fonts (like folders in the finder), inside which are font Families, inside of which are Typefaces. An example of this is All Fonts ▸ American Typewriter ▸ Bold. Collections can be handy if you often find yourself using the same few fonts. You can create your own collections, or use the ones Apple has provided. The Fun collection includes some excellent fonts for parties and cards. If you would like to add a font to the collection, simply drag it in. Adding or deleting collections is controlled by the plus and minus buttons below the collections.
If you find yourself unable to find a font you know is on your computer, make sure you have selected the All Fonts collection. Size is controlled by the slider list and box to the right of the window. You can enter in a value into the upper box, find a commonly used size in the list, or move the slider until you are happy.
There is also a search field at the bottom of the window. If you find that scrolling through all of your fonts takes longer than you want, simply type the name of the font into the search field and it will instantly pop up in the Family column.
Things like shadow, underline, color, and strike-through are controlled by the buttons on the top of the window, as well as from the Format ▸ Font menu.