The source editor supports command completion. Type the first few letters of a word and hit the escape key. The remaining letters will be entered. Hitting escape again will cycle through all possible completions.
TeXShop stores these completions in a Completion file, which can be edited within the program. To add a word to the dictionary, select the word and choose "Add Word" in the Completion submenu of the Source menu. Select "Open Completion File" in this Completion submenu to open the file for direct editing. Notice that completions can be more complicated than just a single word; special commands are available to place the cursor in a convenient spot after completing the command. Examine the Completion file for details.
Command completion can deal with complicated commands with multiple parameters. For example, type "\newcom" and hit escape several times to reveal versions of this command with two, three, or four arguments. Select the command with four arguments. Notice that the cursor is placed on a centered dot --- that is, a mark --- where the first argument will go. The mark is selected, so when you start typing, you'll replace the mark with desired text. When that entry is complete, select the "Next Mark" command in the Completion submenu. This command has a keyboard shortcut, so after practice it can be selected without going back to the menu. The cursor will skip to the second mark and select it. Typing immediately replaces the second mark with desired text there. Continue until all four arguments of the command are filled in.
The current extensive Completion file was written by Herbert Schulz, who added various "Mark" commands to TeXShop. Schulz wrote an extended document describing this facility. That document is available in ~/Library/TeXShop/CommandCompletion.