You do not have to pay tax on any earnings inside a TFSA. Quoting Wikipedia's article, "Investment income, including capital gains and dividends, earned in a TFSA is not taxed, even when withdrawn." This is backed up by the official TFSA government site, http://www.tfsa.gc.ca/, which states, "Investment income earned in a TFSA is tax-free."
This makes the TFSA an appropriate vehicle to store investments which produce dividends. For example, if you invest $5500 and receive a total of $500 in dividends this year, you will not pay tax on that $500, either in this tax year or even subsequently, when you withdraw money out of your TFSA.
Of course, TFSAs aren't meant to be used for regular withdrawals. If you are planning on investing $5500 this year and withdrawing the dividends, I'd urge you to be careful and consider if this is actually the best sort of savings vehicle for you. But that's really just a general warning, nothing specific to dividends. It is possible to do this. Indeed, withdrawing $500 in dividends this year will increase your available contribution room in the next tax year (not in this tax year).
For example, you contribute $5500 at the beginning of this year. By the end of November, you have accumulated $500 in dividends. You withdraw these in December. In the following tax year, you can recontribute this $500 in addition to the standard $5500 contribution room. So, you could contribute $6000. Just be careful with your calculations; I messed mine up and ended up paying a rather substantial penalty for my overcontribution.