All the answers given using LIKE
are totally valid, but as all of them noted will be slow. So if you have a lot of queries and not too many changes in the list of keywords, it pays to build a structure that allows for faster querying.
Here are some ideas:
If all you are looking for is the letters a-z and you don't care about uppercase/lowercase, you can add columns containsA .. containsZ and prefill those columns:
UPDATE table
SET containsA = 'X'
WHERE UPPER(your_field) Like '%A%';
(and so on for all the columns).
Then index the contains.. columns and your query would be
SELECT
FROM your_table
WHERE containsA = 'X'
AND containsB = 'X'
This may be normalized in an "index table" iTable with the columns your_table_key
, letter, index the letter-column and your query becomes something like
SELECT
FROM your_table
WHERE <key> in (select a.key
From iTable a join iTable b and a.key = b.key
Where a.letter = 'a'
AND b.letter = 'b');
All of these require some preprocessing (maybe in a trigger or so), but the queries should be a lot faster.