Like wle said, you want horizontal (track ends) or semi-horizontal dropouts ideally.
To make it work with vertical dropouts, you'd need to use either an eccentric bottom bracket or an eccentric rear hub. White Industries manufactures these, and they are expensive. Unless you're highly dedicated to this frame and have money to blow, this is the wrong frame for your project.
If you do want to proceed, you'll need either a custom rear wheel built around the eccentric hub, or you'll buy the eccentric BB in the appropriate size.
In addition, you'll need:
Front wheel, either road or track. If you run a front brake, which you should, you'll want a rim with a machined braking surface.
Fixed cog w/lockring in appropriate ratio. Not all hubs include a lockring.
Singlespeed crankset with appropriate chainring. You'll need to calculate your ideal ratio. 165mm or 170mm crank arms are best.
Chain. You can use a heavier, noisier 1/8" chain with any fixed cog/chainring combo, but 1/8" cogs or chainrings won't accommodate lighter, quieter 3/32" chains.
Pedals with foot retention: either clips w/straps or clipless
Brake(s). You'll need one or two levers and calipers. If you run two brakes, you need a braking surface on the rear rim, too. This rules out most of the funky, colorful deep-V rims you see around.
Cable. Included with some brake levers.
Bar, either chopped riser, track drop, or road drop. Levers will need to match the bar type.
Stem. You choose the size and type according to the bar and riding position desired.
Grips or bar tape
Saddle and seatpost
Tubes, tires and rim tape
