First, storing an array in a database is only a good idea if you never ever ever have to use the data inside the array for queries on that database itself.
ie: in a library system: do not use an array to store the id's of the books that any person has taken out.
If you need to use the data inside the array for queries then you should change your database design. Read more about that here:
http://www.hvt-automation.nl/yapf/index.php?cmd=viewitem&itemid=21 (comments welcome)
Second, the type would be some string type that is large enough to hold the length of the string, a simple TEXT will do for most cases.
The best way for adding a value... there is only one way, fetch the serialized string from the database, unserialize it, add a value to the array, serialize the array into a string, and update the database with that string.