Hmm. Well if you're storing the first and last names in different columns of the table then you would just do a wildcard on each one (or on one but not the other, or whatever you want to do).
SELECT * FROM `table` WHERE first_name LIKE 'Ri%' AND last_name LIKE 'Smi%';
Otherwise you're looking at using "regular expressions" (check google if you're not familiar with these) to get the job done. Those can be pretty sophisticated but also pretty difficult to create. There is MySql syntax for this:
SELECT * FROM `table` WHERE first_name LIKE 'Ri%' AND last_name = 'Smith';
Regular expressions are pretty neat though.