1、As 就是关系代词,指代后面的句子honesty is the bestpolicy.
2、As an oldsaying goes 是前置的非限制性定语从句,其结构如下：
主语：an old saying
谓语动词：goes【此处的 go 是及物动词,相当于 say 的意思】
宾语：as
3、As 也可以用下面宾语从句代替来理
An old saying goes that "honesty is the best policy".（= An old saying says that"honesty is the best policy"）
4、As指代后面要提到的或前面已经提到的一个句子,用来引导的定语从句,在从句中充当宾语、主语或表语.另如：
As you can see,we're still working. 如你所见,我们仍在工作.【as 指代 we're stillworking,在从句中作宾语,等于含有宾语从句的 you can see that we're still working 所表述的意思】
We were sitting, as I remember,in a riverside restaurant.我记得我们当时是坐在一个河畔的餐馆里.【= as 指代 we were sitting in a riverside restaurant,在从句中作宾语,等于含有宾语从句的I remember that we were sitting in a riverside restaurant 所表述的意思】
The statement reads in full as follows:… 声明全文如下：…… 【as 指代 the statementreads in full,在从句中做主语,等于含有主语从句的 That the statement reads in full follows … (全文) 所表述的意思】
We're busy enough as it is.我们实际上很忙.【as 指代we're busy enough,在从句中作表语,等于含有表语从句的 It is that we're busy enough 所表述的意思】