Learn Russian: Этот суп стоит пятьдесят два рубля.

In Russian, the case of the noun after a compound number depends only on the last word of that number. Since пятьдесят два ends in два (two), it follows the rule for the number 2: the noun must be in the genitive singular. So, the dictionary form рубль becomes рубля.

I see a soft sign (ь) in the middle of пятьдесят. Is that normal for tens?

Yes, for the numbers 50, 60, 70, and 80! These words were formed by mashing together a single digit (like пять) and an old word for ten (десят). You keep the soft sign from the first word right in the middle, but notice there is no soft sign at the very end of пятьдесят.

If the item cost 52 kopecks (копейка, feminine) instead of rubles, would the number change?

Yes, the very end of the number would change! The number 2 has different gender forms. The пятьдесят part stays exactly the same, but два (masculine/neuter) changes to две for feminine nouns. So, 52 kopecks would be пятьдесят две копейки.

The verb стоит looks exactly like the word for "stands". How do I know which one it is?