Dan, first of all, let me say that I haven't fished Hat in quite a few years.  However, I do have quite a bit of experience with Hat during the May-June time frame.  I presume that you will be fishing the Hat 2 area.  If so, here are some suggestions.  For a reliable nymph, try a #16 Sawyer PT in natural or dyed green (the green looks unnatural, but works well).  Fish it below an indicator like you would Putah.  Don't be afraid to try it even in the meadow water.  For dries, you'll want to have #16 Little Yellow Stones, #16 Quigley Cripples,  #18 Rusty Spinners, #16 Olive Caddis Variants, #18 Creamy Orange Paraduns, and #16 bright orange paraduns.  If the LY Stones are hatching, the rises are splashy and you'll see the stones in the air.  Early and late if you see fish sipping something off of the surface, try the Rusty Spinner.  I don't know if it's still true, but Hat used to be the best the last hour before dark.  The stream would literally come alive and the fish were easiest to catch in the dim light.  That's when you can use the Quigley Cripple.  When it get's really dark, put on the bright orange paradun.  The bright color makes it easy to see in the low light.  Hat used to have a green drake hatch; if it still does, you can try a #12 Adams.  Hat also used to have a giant stonefly hatch (Pteronarcys) in early May.  For it you may want to try a big stonefly pattern.  You may want to stop by the Fly Shop in Redding to ask about what flies they would suggest.