The word for “Saturday” in German is “Samstag.” This word, like all days of the week in German, is capitalized because it is a noun. The day of the week itself is associated with rest and free time, as for many people Saturday is a time for fun and meeting friends.
Rules:
Am Samstag is an expression that is used to say “on Saturday”. It is the standard way when referring to a specific event that takes place on that day.
Am Samstag gehe ich ins Kino. (I'm going to the movies on Saturday.)
Samstags is the form used to say “on Saturdays” when referring to something that happens regularly.
Samstags besuche ich meine Großeltern. (On Saturdays, I visit my grandparents.)
If you want to say “every Saturday”, you use “jeden Samstag”.
Jeden Samstag gehe ich auf den Markt. (Every Saturday I go to the market.)
Examples:
Am Samstag mache ich meine Hausaufgaben. (On Saturday I do my homework.)
Samstags gehe ich meistens einkaufen. (On Saturdays I usually go shopping.)
Jeden Samstag treffe ich mich mit meinen Freunden. (Every Saturday I go out with my friends.)
This is how the word “Samstag” is used in German! It's important to remember that it is always capitalized, and the forms “am Samstag,” “samstags,” and “jeden Samstag” help to convey exactly what is happening on that day.