The Swiss have it easy: they completely eliminated the ß (eszett or "sharp s") some years ago, but since we are teaching Standard German at Yabla, we should learn a few general rules about which words use s, ss, and ß.

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1. Single s
There are no words in German that begin with ss or ß, so that rule is easy. A single s will usually come after the letters l, m, n and r when a vowel follows the s, with words such as: der Balsam (the balm), die Bremse (the brake), and sparsam (economical):

Das ist sehr sparsam!

This is very economical!

Caption 38, Der Trabi - Das Kultauto aus dem Osten

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A single s will usually come before the letter p, with words such as raspeln (to grate), lispeln (to lisp), and die Knospe (the bud):

Knospen, Blätter oder, Früchte von Platanen zum Beispiel...

Buds, leaves or, fruit from the plane trees, for example...

Caption 26, Freilebende Papageien - Überwintern in Wiesbaden

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In most cases, only a single s will come before the letter t, with words such as die Liste (the list), pusten (slang: to blow), and prusten (to puff):

Dann will ich husten und will prusten

Then I'll huff and I'll puff 

und euer Haus zusammenpusten!

and I'll blow your house down!

Caption 50, Märchen - Sagenhaft - Die drei kleinen Schweinchen

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2. Double s
The double s is usually written only after a short vowel, with words such as das Schloss (the castle), ein bisschen (a little bit), and passend (fitting):

Eigentlich hätte es gar keine passendere Rolle für sie geben können.

Actually, there couldn't at all have been a more fitting role for her.

Caption 16, Christina Aguilera und Cher - in Deutschland

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3. Eszett: ß
The ß is usually used after a long vowel or double-vowel combination (dipthong), in words such as die Straße (the street), der Meißel (the chisel), and stoßen (to bump, to repel):

Gut, und die stoßen sich ab.

Good and they repel one another.

Caption 35, Das 1. Newtonsche Gesetz - erklärt am Beispiel des Dodomobils

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4. Verbs that vary between ss and ß
Just to make it more complicated, there are some verbs that are written with ß in the infinitive, but switch to ss when conjugated — and vice versa too! For instance the verb vergessen (to forget) uses the letter ss in the infinitive and present tenses (ich vergesse, I forget), but switches to the ß in the past (preterite) tense:

Belle gewann das Biest so lieb,

Belle became so fond of the Beast

dass sie seine äußere Erscheinung darüber völlig vergaß.

that she fully forgot about his outward appearance.

Captions 61-62, Märchen - Sagenhaft - Die Schöne und das Biest

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Further Learning:

Do a search on Yabla German and see if you can find some more examples of verbs that vary between ß and ss in their infinitives and their conjugations.