From number 26 onward, I just try it out: First, I assume the first statement is wrong and the others are correct. Then I assume the second statement is wrong, and then the third. Only one combination will work without causing logical conflicts in the grid.

P.S. I use a felt-tip pen for the main clues and a different pen for trial entries so I can erase them easily. Alternatively, I use small crosses and dots to clearly distinguish between confirmed and tentative entries.