I'm no DB guru, but basically you'd only have the first UPDATE query you perform now.
When SELECT'ing data, you want to pull data from the other table. So, let's pretend we have been given a certain item ID and we want to display information about that item as well as what category it's in (I don't know your DB design/application, so I'm just making up a scenario here). Your query would look something like this:
SELECT item_description, item_name, cat_name
FROM items i
JOIN categories c ON i.cat_id = c.id
WHERE i.id = $id
EDIT:
David P wrote:Should I change "cat_name" in the Items table to "cat_name_id" and "varchars" type to "int"?
I used cat_id in my example query above, but you can use whatever column name makes sense to you. As for the type, I would match whatever type of column the 'id' column in the categories table is (minus the AUTO_INCREMENT value, obviously).
EDIT2: DB guru's - I moved this thread into the DB forum in case any of you see something wrong with my suggestion... feel free to poke fun at my lack of SQL knowledge! :p