What is the best way to translate sentences like this:

チャーチには たくさんの 巡礼の 人が いた そうです。

Chaachi ni wa takusan no Junrei no hito ga ita soo desu.

I know that:

Chaachi = church

takusan = many or a lot of

junrei = pilgrimage

hito = people

How should I deconstruct this sentence?

junrei no hito = the people of pilgrimage?

takusan no junrei no hito = the people of pilgrimage of ....?!

I'd translate "takusan no" as "many" and "junrei no hito" as "people on pilgrimage" or simply "pilgrims".

Remember too that の can be used simply to describe a noun with another noun; no reason to mechanically translate into English as 'of'. There are plenty of cases, such as this one, where that will produce essentially meaningless English sentences.

たくさんの人 is just 'many people' and たくさんの巡礼の人 is just 'many pilgrims' or 'many people on a pilgrimage.'