Learn Spanish (Latin America): Yo pienso empezar el negocio.

Pensar (to think/plan) is a stem-changing verb. In the present tense, the e in the middle of the verb changes to ie for most forms, including the "I" form, which gives us pienso.

Doesn't pensar mean "to think"? Why is it translated as "I plan" here?

You are right that pensar usually means "to think." However, when you use pensar followed directly by an infinitive (an unchanged verb, like empezar), it takes on the meaning of "to plan to" or "to intend to" do something. So, pienso empezar means "I plan to start."

Empezar is also a stem-changing verb. Why doesn't it change to empiezo in this sentence?

When two verbs are used together to form a single idea (like "plan to start"), only the first verb is conjugated (changed to match the person). The second verb always stays in its full, unchanged dictionary form. Since pienso is already conjugated to match "I", empezar stays exactly as it is.

Do I have to include the word yo at the beginning?