This is a mistake that occurs very often (especially on the internet) in spite of the fact that it can be easily avoided.
The most simple way to dodge this uncomfortable situation (where you have to pick between your and you’re) is realizing that you’re is a short form for you are. So just replace the two. If your phrase still makes sense, then you already picked the right form.
Example: This is you’re book. You’re happy to read it.
Example (replaced): This is you are book. You are happy to read it.
As you can see, only the second sentence still makes sense after replacing you’re with you are, so – in that case – we have chosen the correct form.
We can also approach this from another angle by realizing that your is a pronoun that shows possession. That being said, we can use the same method of replacing, but this time we will use another possessive pronoun (for example my). The same principle applies: if the phrase still makes sense, then the correct form is your, otherwise it’s you’re.
Example: Your right! This is your pencil.
Example (replaced): My right! This is my pencil.
Thanks to BlueEnergy for proposing this topic. It was also on my to do list, but it’s nice to see that some else cares.