As soon as I got your letter, I started looking through a newspaper to find a good advert.

looking 是动词 look 的现在分词形式，look 的基本意思是"看"。 through 是介词，表示"穿过、通过"，在这里引申为"从头到尾地"。 looking through 这个短语表示"翻阅、浏览"，指快速查看内容以寻找特定信息。