Learn Swedish: Jag hatar att vänta.

Swedish doesn't have an "-ing" form (a gerund) that acts like a noun. When you want to say you hate or love doing an activity in Swedish, you use att (to) plus the infinitive form of the verb. It is grammatically identical to saying "I hate to wait" in English.

Do you pronounce att the way it is spelled here?

Usually, no. In everyday spoken Swedish, the infinitive marker att is almost always pronounced like the Swedish letter "å" (which sounds a bit like the "o" in "sore"). So this sentence will usually sound like "Jag hatar å vänta".

Could I drop the att and just say Jag hatar vänta?

No, you need the infinitive marker att here. While Swedish has some helper verbs like vill (want) or kan (can) that let you attach another verb directly without att, verbs expressing preference like hatar (hate), älskar (love), or gillar (like) always require it.