To add a new payment logo, first you need to upload your image using the Content Editor. Go to Content->Edit Templates and browse to reboot/images/payment. Near the bottom of the page, you'll see Upload a file to the current directory. Click on Choose File and browse to the file on your computer and select it. Click Upload to add your image. Now browse to reboot/custom and find payment_logos.tpl. Click on it to edit it and add the following:
<li><img class="lazy" src="{$AltImagesDir}/spacer.gif" width="60" height="38" data-src="{$AltImagesDir}/payment/yourimage.png" alt=""></li>
replacing 'yourimage.png' with the actual name of the image you just uploaded.