Being polite will always get you farther than anything else, so start with the basic phrases of politeness: "Gracias," which means "Thank you," and "Buenos dias," which means "Good morning."
You should also know how to say "I'm sorry" and "Excuse me": "Disculpe," or "Mis disculpas," is similar to "my apologies." For "Excuse me," you can say "Con permiso."
Another useful phrase is "Donde esta...?" or "Where is...?" We always need to know how to ask for directions. We should also know the directional words "izquierda," (left), "derecha," (right) and "cuadras" (blocks). It's also important to know "Estoy perdida," which means "I am lost."
When shopping, it's imperative to know how to ask "Cuanto cuesta?" or "How much does it cost?" Knowing how much things are is quite important before you have misunderstandings. Be familiar with the local currency and money.
The other phrase that can come in handy is "Necesito ayuda," or "I need help." We always have to know when to ask for help, especially in important situations.