Do I need to speak the language where I want to go?

Generally speaking, yes.  But it depends on what you do and where you go.  

English teachers don't need to know the local language and employers often prefer that they don't know it - they want them to teach in English.  Nurses, doctors, IT people and others are often hired in the Middle East if they are fluent in English - the common language that many people share there.

If you want to teach English, your native speaker language skills are why you are hired: Your accent, your native ability to know what grammar is wrong or right, your ability know what sounds right or wrong in common usage.  Time and experience (or a good TEFL certification course) will give you the ability to explain these things - but in the beginning, even if you can't explain it - you will still know what is wrong and what is right. 

 How will I find my way around and/or buy the things I need if I am not fluent in a local language?

This is not that much of a problem.  Most employers will assign a coworker or a staff assistant to help you do the things you need to do - until you learn the basics.  After you live and work in a few countries, you will find yourself quite skilled at finding what you need, using either very basic language or even just gestures. 

After all, you will most likely NOT be your employer's first foreign employee - and they will likely be familiar with most of your wants and needs - from finding food you are familiar with, to cold remedies, Internet cafes, or even good restaurants.

Of course, learning to count money and give taxi drivers directions quickly, will make life much easier for you.  But those simple skills are not usually difficult - even in Chinese!