This userscript will hide promoted tweets on twitter.
It adds a css rule to hide the promoted tweets. It is cross-browser compatible, and it will auto-update if a newer version of this script is published.
The easiest way to install the script is to first have GreaseMonkey (Firefox) or TamperMonkey (Chrome, Safari, Opera). If you have those addons installed already, simply open the script and follow the prompts to install it.
For more detailed steps, follow these instructions for your particular browser.