Use the plural form "Saturdays" to talk about every Saturday or "Saturdays" in general.
When talking about every Saturday or "Saturdays" in a general way, we commonly use the plural form (Saturdays).
On Saturdays, my family and I gather around the kitchen table to enjoy a delicious breakfast together.
Alternatively, you can use the singular (Saturday) in this situation. For example, if you are asked:"Would you like to come to a party on Saturday?" You can answer the following:
I always visit my uncle on Saturday/Saturdays.
Both options, the singular and the plural, are correct in the example above. The sentence contains an adverb of frequency ("always") and a verb in the simple present. Other common adverbs of frequency that you can use are: frequently, generally, typically, normally, often, usually, seldom, rarely, etc.
My friends and I often plan outdoor adventures on Saturdays/Saturday.
When using Saturdays at the start of a sentence and referring to every Saturday, we recommend the plural form to avoid ambiguity or confusion:
On Saturdays, Sarah volunteers at the local animal shelter.
When talking about a specific day, however, always use the singular form.
We had a big party on Saturday.
We had a big party on Saturdays.
You can follow the same strategy with the rest of the days of the week: