1. Built-in Short Cuts:
When you pull down the menu items you see the keyboard shortcuts. Here is an example of the Source menu:

2. Command Completion:
If you simply start typing the command you want

hit esc you get:

Hitting esc again:

3. Abbreviations:
Besides command completion there are also abbreviations.
All abbreviations for environments start with a ‘b’.
For example if you type \bite and hit esc you get the itemize environment:

4. System Preferences:
Furthermore, you can always add your own keyboard shortcuts. For example going to System Preferences → Keyboard, you can define the COMMAND-B option to select the Bold pull down (which does not have a keyboard shortcut defined):

After restart, COMMAND-B yields:

5. Key-Bindings Editor
Under the Source → Key Bindings you can access the key-bindings editor with which (I assume, have not tried this myself) you can set up other keyboard sequences:

From Page 6 of the TeXShop Tips & Tricks which can be accessed from the Help menu:
e.g. pressing Opt-, with a US keyboard layout, usually enters ≤ into your document but with Key Binding enabled \leq will be entered. Similarly, with some text selected pressing " will surround the selected text with `` and ''.
6. Macros Editor:
From Page 7 of TeXShop Tips & Tricks:
Text macros are simple text substitutions. You can also tell TEXShop to insert any selected text using #SEL#, place the cursor using #INS# and even put in multiple lines in the macro itself. Then you can assign the text macro to a keyboard shortcut.
I like to use Cmd-B and Cmd-I to insert \textbf{...} and \emph{...} into the document where ... is any possible selected text. Macros to do that are already under the Macros → Text Styles Menu so we need only assign keyboard shortcuts to them. To assign Cmd-I to the emphasize macro: open the Macro Editor where the form of the Macros menu appears in the left hand pane; click the emphasize macro found under Text Styles; click the Key insertion box and simply insert a lower case ‘i’ (the Cmd key is assumed and additional modifier keys can be checked off ).
