Make yourself appear offline
In Steam simply use the drop down next to your name in the friends list and select 'Offline' - this will make you appear offline to everybody on your friends list and prevent the sending of the notifications when you log in/out or start playing a game;
Setting offline mode will prevent you from chatting with any of your friends, and them from chatting with you also. Your friends list will change to show a 'sign in' button and detail that you are currently 'offline';
Make yourself appear offline by default
It is possible to prevent the Steam client from logging into Friends in the Steam settings by clicking on the Steam menu in the main client window, followed by settings and then unchecking 'Automatically sign into Friends when I start Steam' on the 'Friends' tab;
It's worth noting that this is not the same as putting your Steam client into 'offline mode', and still requires an active connection to the internet for Steam to work properly. You're also still able to update and download new games - the chat functionality, friends list and game notifications are the only aspects of the Steam client affected by setting your status to 'offline'.