Hey mac, the best thing to do is to take your vest into local a shop and let them fix you up with what you might need based on conditions in whatever section of the Provo you plan to fish. This time of year, if the river is blown out in the upper sections by snow melt, you might want to go with sculpin patterns etc, but you should be getting golden stones and skawala stones soon- big nymphs and dries might be good, but the locals will know whether or not it's happening.
Typical stuff you might need:
license
spools of mono tippet (4X, 5X and 6X)
leader knotless 9' mono leader tapered to 4X
fly flotant
split shot
indicator
nippers ( or fingernail clippers)
hemostat to crush barbs and remove hooks, or a pair of needle nose pliers on a lanyard (or taped to a cord so you don't lose them.)
flies- local shop can hook you up, and will be the best source of info. A distant second might be a site with stream reports like this one:
Trout Bum 2 : Fly Fishing Reports : Provo River, Green River, Weber River, L.C. Ranch, Utah Flyfishing Report - Park City, Utah
It might be tough to fish without waders because of trees behind you- maybe there will be enough left over for a cheap pair of rubber hippers?
good luck,
mark