How to make multiple counts in one query?

To get a count for each of those you can try

SELECT
    COUNT(CASE WHEN `col1` LIKE '%something%' THEN 1 END) AS count1,
    COUNT(CASE WHEN `col1` LIKE '%another%' THEN 1 END) AS count2,
    COUNT(CASE WHEN `col1` LIKE '%word%' THEN 1 END) AS count3
FROM `table1`; 

Similar to Aaron's solutio, shorter syntax:

SELECT
    SUM(col1 LIKE '%something%') AS count1,
    SUM(col1 LIKE '%another%') AS count2,
    SUM(col1 LIKE '%word%') AS count3
FROM `table1`

The LIKE expression makes for a boolean result. TRUE is 1, FALSE is 0, so the CASE is redundant here.