FTS does not support LIKE
The previously accepted answer was incorrect. Full Text Search with its full text indexes is not for the LIKE operator at all, it has its own operators and doesn't work for arbitrary strings. It operates on words based on dictionaries and stemming. It does support prefix matching for words, but not with the LIKE operator:
Trigram indexes for LIKE
Install the additional module pg_trgm which provides operator classes for GIN and GiST trigram indexes to support all LIKE and ILIKE patterns, not just left-anchored ones:
Example index:
CREATE INDEX tbl_col_gin_trgm_idx ON tbl USING gin (col gin_trgm_ops);
Or:
CREATE INDEX tbl_col_gist_trgm_idx ON tbl USING gist (col gist_trgm_ops);
Example query:
SELECT * FROM tbl WHERE col LIKE '%foo%'; -- leading wildcard
SELECT * FROM tbl WHERE col ILIKE '%foo%'; -- works case insensitively as well
Trigrams? What about shorter strings?
Words with less than 3 letters in indexed values still work. The manual:
Each word is considered to have two spaces prefixed and one space
suffixed when determining the set of trigrams contained in the string.
And search patterns with less than 3 letters? The manual:
For both LIKE and regular-expression searches, keep in mind that a
pattern with no extractable trigrams will degenerate to a full-index scan.
Meaning, that index / bitmap index scans still work (query plans for prepared statement won't break), it just won't buy you better performance. Typically no big loss, since 1- or 2-letter strings are hardly selective (more than a few percent of the underlying table matches) and index support would not improve performance to begin with, because a full table scan is faster.
text_pattern_ops for prefix matching
For just left-anchored patterns (no leading wildcard) you get the optimum with a suitable operator class for a btree index: text_pattern_ops or varchar_pattern_ops. Both built-in features of standard Postgres, no additional module needed. Similar performance, but much smaller index.
Example index:
CREATE INDEX tbl_col_text_pattern_ops_idx ON tbl(col text_pattern_ops);
Example query:
SELECT * FROM tbl WHERE col LIKE 'foo%'; -- no leading wildcard
Or, if you should be running your database with the 'C' locale (effectively no locale), then everything is sorted according to byte order anyway and a plain btree index with default operator class does the job.
More details, explanation, examples and links in these related answers on dba.SE:
