I solve it using basic Tamil grammar. For example, the start of a word cannot be a consonant ("mey ezhuththu") etc.
I start with the smaller words (2 or 3 white squares between black squares) and build the whole paragraph word by word. As I complete a meaningful sentence or set of sentences emerge.
Here is an earlier one which is also of smaller number of letters.
Here let us take the 3 letter word at the end of the 4th row. As I look up the 3rd column from the right, I find the first letter can be either "va" or "pO". Then I look up the letters in the next column to see it can be van(th) or "pOnA"; then from the last column, I can conclude the word to be either vantha of p"nAl/pOnAr". Continuing like this, I get the final construct.
For this one, you will also find the answer in the comments, which will help you understand how these work.
Also, to exchange "pO" with "n(th)" in the (3rd from right) column, just click on "pO" to see it highlighted and then click on "n(th)".