Sometimes it's good to just set the record straight, and with that intention, let's take a look at zählen and zahlen. Short and sweet: zählen is "to count," and zahlen is "to pay."
Sie zählen die Stimmen nach dem Ende der Wahl.
They count the votes after the end of the election.
Caption 4, Bundesrepublik Deutschland - Einbürgerungstest - Part 6
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Das macht zusammen vierzig Euro fünfzig. Zahlen Sie bar oder mit Karte?
All together that is forty euros and fifty cents. Will you be paying in cash or with a card?
Caption 7, Nicos Weg - Folge 16: Zahlen, bitte!
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Although you might be able to come up with a mnemonic device that you find helpful, simply remembering that Ich möchte zahlen means "I would like to pay" may be enough to help you sort it out. At the same time, you might still find that you get flustered mid-sentence trying to remember which verb is correct. It doesn't help that the noun die Zahlen means the "the numbers." It is the plural version of the noun die Zahl:
Der Adventskalender hat vierundzwanzig Türen, und auf jeder steht eine Zahl.
The Advent calendar has twenty-four doors, and each one has a number on it.
Caption 11, Eva erklärt - den Adventskalender
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In English, "to count" can also mean "to matter." Zählen is also used to mean "to count," "to count as" or "to number among." Take a look at these examples:
Beim Blocken zählt jede Sekunde.
When blocking, every second counts.
Caption 37, Olympische Spiele - Beachvolleyball
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Sie zählt mit zu Deutschlands erfolgreichsten Sängerinnen.
She is counted among Germany's most successful singers.
Caption 2, Cassandra Steen - Geheimnis für positive Energie
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And one final note: you probably have wondered what the difference is between zahlen and bezahlen. The truth is that they are often interchangeable, but there are some instances where zahlen is wrong. For example, when you speak about paying a person for a service, you would generally use bezahlen and not zahlen.
Further Learning
Look up the meanings of the related verbs anzahlen, zurückzahlen, and auszahlen, and search Yabla German to find them used in a real-world context. Some words related to zählen are die Volkszählung ("census") and der Stromzähler ("the electricity meter").