It seems like when I encounter an “st” at the beginning of a word, like in “Stimmt” or “Straße”, it’s pronounced “sht”, and in “Vorspeise”, it’s “shp” even though it’s not at the start of the word. In other words like “fast”, it’s just “st”. Is there a hard-and-fast rule for when to use which pronunciation?
It depends a lot on the dialect. You can identify native speakers from southern Germany because they (or we 
) pronounce nearly everything like “sh”. In northern Germany the pronunciation is more like “st”. So we say “fashd” instead of “fast”…
The general rule is pretty easy to remember: if sp or st are at the beginning or in the middle of the word, then it’s pronounced sh. If it’s at the end of a word, then it isn’t sh.
This is why it’s Sh-traße and Vor-sh-peise, but fast and du bist don’t have that sh sound. However, some words have developed a different pronunciation over time, like am besten (no sh in Hochdeutsch). It doesn’t always apply to compound words, but that’s another topic 
Hope that helps!
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st and sp don’t have the sh sound
- if they are NOT in the same syllable: ges-tern, bes-ten
- if they are in different parts of the same word, like in “trennbaren Verben”: aus-packen, aus-parken
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@mojombo and all other dear German students: With this beautiful information when to pronounce it how, let’s go ahead to the practice:
- Siebzehn Schnitzer, die auf siebzehn Schnitzsitzen sitzen und mit ihren spitzen Schnitzern Ritzen in ihr Schnitzholz schlitzen, wobei sie schwitzen, sind siebzehn schwitzende, schnitzende, auf dem Schnitzsitz sitzende, spitze Schnitzer benützende Schnitzholzritzenschlitzer.
- Ein Stachelschwein, ein Stachelschwein, das muss ein Schwein mit Stacheln sein, doch hat es keine Stachelein, so ist es auch kein Stachelschwein.
- Der Streusalzstreuer zahlt keine Streusalzstreuersteuer, keine Streusalzstreuersteuer zahlt der Streusalzstreuer.
YES, YOU CAN!
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Love the tongue twisters Stephan!