In Burning Board Lite 2, you have to download the desired templates via FTP and edit them, yes.
The templates are located in:
/templates
/wcf/templates
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you will need ftp yes if you don't have a file manger with your hosting. and yes the above places are where you add the ads
public_html/templates/header.tpl(and footer.tpl) is where i had my ads on my forum. you can just mess around with the placement on them two files. i just stuck the google adsense code right at the bottem of footer.tpl and put the ad code somewhere in the middle of header.tpl (it depends where you want to show)