SELECT * FROM tb_name WHERE tb_column LIKE '%word%'
The * can be replaced with column names seperated by a comma. It's much better with tables with lots of columns to only select the ones you need. You should also do it if you only need one or two columns in your code. Doing so will speed up your queries and reduce resource usage.
The db_name should be the table you are looking to use.
The db_column should be the column you are hoping to match records with. If you need more than one, seperate them by the word AND
...WHERE first_name LIKE '%john%' AND last_name LIKE '%smith%'
LIKE is used for string matches. The % matches zero or more characters and I think it's either . (period) or _ (underscore) for matching one character only. You should be careful on how you use the %, and if you need to put it at the end and the beginning of string searches. You also need to be careful on case as it's case insensitive (by default). So in your PHP (guessing?), you might want to use strtolower($input_string) to convert input to lower case, and then in your SQL put
WHERE LOWER(first_name) LIKE '%john%'
You can just use =, <, > for numbers and they don't need to enclosed in ' (single quotes). Strings need to be enclosed in quotes, numbers don't.
Probably more information than you need at the minute though