Learn Swedish: Köper kvinnan sockret idag? - Does the woman buy the sugar today?

Socker (sugar) is an ett-word that ends in an unstressed -er. When we add the definite suffix -et to make it mean "the sugar", we drop the e in -er to make it easier to pronounce. So, socker + -et becomes sockret.

Why does the sentence start with the verb Köper?

In Swedish, you turn a statement into a yes/no question by putting the verb first. There is no equivalent to the English helper word "does". So instead of "Does the woman buy...", the Swedish sentence literally says "Buys the woman...".

How do we know kvinnan means "the woman" rather than just "woman"?

Kvinna is an en-word ending in a vowel. To make it definite ("the woman"), we just add an -n to the end, making it kvinnan.

Is "today" always written as one word (idag) in Swedish?

You will see it written both as one word (idag) and as two words (i dag). Both are completely correct and common in Swedish, though the one-word version is very popular in everyday writing.