Learn Spanish (Spain): Tengo que estudiar para el examen.

In Spanish, when you want to say you "have to" do something, you use the verb tener (to have) followed by que and then an infinitive verb (a verb in its basic form, like estudiar). If you leave out que, tengo just means you own or possess a physical object.

Why isn't the word yo (I) at the beginning of the sentence?

In Spanish, the ending of the verb usually tells you who is doing the action. Tengo specifically means "I have", so you don't need to add yo unless you want to add extra emphasis or clear up confusion.

Why is estudiar in its full dictionary form instead of being conjugated?

The rule for the tener que structure is that the second verb must always be in the infinitive (the basic, unchanged form ending in -ar, -er, or -ir). Since tengo already tells us who has to do the action, estudiar stays exactly as it is.

I've seen both por and para used for the English word "for". Why is it para here?

You use para when talking about a purpose, a goal, or a deadline. Here, the exam is the specific reason or goal for your studying, so para el examen is the correct choice.