Adding HTML

Help. I am very new to WP and building sites, so some of the tech talk is confusing to me.

I want to add some basic html to my wordpress blog, such as adsense links and a statcounter. I’ve tried pasting the html into the body of a post – no luck. Also no luck with adding the html via a text widget. In both cases, it seems to partly disappear when I hit “publish” or “save”, and it doesn’t show up on the site. I upgraded to a paid domain, thinking maybe that would help. No dice. I do not yet have the knowledge to get into the template and make changes there (nor does it seem possible to get in and save changes). My site is liveukulele.com

Can anyone offer any help?