To pledge to a project, just click the green “Back This Project” button on any project page. You will be asked to input your pledge amount and select a reward. From there, you will go through the Amazon checkout process. Note that you must finish the Amazon checkout process for your pledge to be recorded.
We don't currently have an anonymous pledge feature. You are free to choose any username you wish, though, so you could anonymize that way if you would like. Otherwise, we hope you're okay with showing your name and support.