Learn Swedish: Jag vill köpa snygga byxor. - I want to buy stylish trousers.

Snygga is the plural form of the adjective snygg (stylish/good-looking). Because it is describing a plural noun (byxor), you must add the -a ending so that the adjective matches the noun.

Why is byxor plural if I might just be buying one item of clothing?

Swedish works exactly like English here! We say "trousers" or "pants" in the plural for a single item, and Swedish does the same with byxor. The singular word en byxa exists, but it usually refers to just one pant leg. If you want to specify buying exactly one item, you can say ett par byxor (a pair of trousers).

Why do we use köpa instead of the present tense köper?

Because it comes right after vill (want to). Vill is a helping verb, and the main action that follows it always has to be in its infinitive (dictionary) form. So, instead of the present tense köper (buy/am buying), we use the infinitive köpa (to buy).

Don't I need a word for "to" between vill and köpa?

No, you don't. While the Swedish word for "to" before a verb is usually att, you never use it after vill. The "to" is already built into how the helping verb works, so you just put them directly together: vill köpa (want to buy).